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  • View in gallery

    Evolution of Illinois soil moisture standardized anomalies during and after the 1988 drought, averaged over Illinois Climate Network (ICN) observations. Contour interval is 0.25 standard deviation. Also shown are the standardized precipitation anomalies (bars) for each month.

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    Autocorrelation function of anomalous Illinois root zone (0–0.4-m depth) soil moisture and precipitation. Indices are determined from statewide averages of Illinois Climate Network (ICN) observations for 1985 to 2004, as described in the text. Anomalies are departures from the monthly seasonal cycle, smoothed with a 3-month running mean. (a),(b) Autocorrelation of springtime root zone soil moisture and precipitation, respectively. In both panels, autocorrelation lag is measured from the base FMA (February–April) anomalies; so, for example, a lead of 6 months represents the correlation between FMA and the subsequent ASO season. Dashed blue lines show the observed autocorrelation functions; solid black lines show exponential decay, where the decorrelation (e-folding) time scale is determined from a fit to the entire autocorrelation function. The red dots indicate values that are significantly different (95% confidence interval; see section 3c) from zero. (c),(d) Annual cycle of the autocorrelation function for 3-month running mean root zone soil moisture and precipitation anomalies, respectively. The month ordinate indicates the time of the base season, and the abscissa shows the lead/lag. For example, the (−13, MAM) value in (c) indicates the correlation of MAM root zone soil moisture anomaly with the previous year’s FMA root zone soil moisture anomaly (i.e., 13 months earlier); the (14, FMA) value (magenta oval) indicates the correlation of FMA root zone soil moisture anomaly with the root zone soil moisture anomaly in the next year’s AMJ season (i.e., 14 months later). The diagonal yellow lines therefore represent correlations with the previous FMA (subsequent AMJ) seasons, for any lead/lag. Correlation maxima along these lines are suggestive of reemergence. Note that both magenta ovals represent the 14-month lag correlation between FMA and the following AMJ (one oval forward and the other backward). The horizontal black dashed lines represent the location of the values in the blue dashed lines in (a) and (b). Note that in this and all subsequent plots, vertical dashed gray lines are drawn at 6-month intervals, and stippling represents the 95% confidence interval.

  • View in gallery

    A conceptual two-layer soil moisture model; see text for more details.

  • View in gallery

    Physics of soil moisture reemergence: a demand-driven hypothesis. (a) Soil moisture climatology, variability, and (P − ET)/P* climatology: color shading shows monthly climatology of soil moisture in terms of percentage of saturation as a function of depth from the surface to 2 m. Line contours represent interannual variability using an estimate of one standard deviation from the ICN data. Bars shows P − ET climatology, normalized by annual average precipitation, using LDAS data from CLM. (b) An estimate of two major components: (P − ET − SR) and T, based on data from CLM. Error bars show interannual variability using an estimate of one standard deviation. Note the major contribution of T in the summer season. Units are mm month−1. P* is annual average precipitation.

  • View in gallery

    Physics of soil moisture reemergence: anomaly propagation hypothesis. Both panels depict the conceptual two-layer soil model of Fig. 3, with anomalous soil moisture conditions and the total soil water potential (soil matric potential and gravitational potential with reference at 2-m depth) with anomalous soil moisture in the deep layer and (without loss of generality) climatological conditions in the root zone. (a) A deep layer wet anomaly would lead to a smaller potential gradient between the root zone and the deep layer and consequently a reduced magnitude of T, resulting in a wet anomaly developing in the root zone. (b) A deep layer dry anomaly would lead to larger potential gradient between the root zone and the deep layer and consequently an increased magnitude of T, resulting in a dry anomaly developing in the root zone. Numbers in the parentheses (X ± Y) show the total soil water potential (meters of water) using ICN data for FMA season, where X represents the climatological mean value and Y represents one standard deviation of interannual variability. The hatched horizontal arrow in the deep layer represents the transfer of memory from the previous season to the current season. Filled thick black arrows show total water movement from root zone to the deep layer below. Filled thick red arrows show the drainage term. See text for further explanation.

  • View in gallery

    (top) Root zone soil moisture standard deviation and (lower rows) lag correlation from 3 to 18 months, for MAM base season, 1950–2010, in the (left) NCAR CLM and (right) VIC-highres datasets. Only statistically significant autocorrelations (95% level) are shown using color scale in rows 2–7. Numbers in each panel show the percent of areal coverage of the significant autocorrelations. The outlines of boxes used to define the regional time series (see text and also Fig. A2) are also shown.

  • View in gallery

    Recurrence time scale TR for root zone anomalous soil moisture in DJF, MAM, JJA, and SON base seasons, 1950–2010. Only values of TR for which the recurrence magnitude is significant at the 95% level are shown. (left) TR maps determined from CLM data for (a) DJF, (b) MAM, (c) JJA, and (d) SON. (right) As in left, but for VIC-highres for (e) DJF, (f) MAM, (g) JJA, and (h) SON. The outlines of boxes used to define the regional time series are also shown.

  • View in gallery

    Soil moisture statistics for the SW time series in the CLM dataset, for the years 1950–2010. Annual cycle of the autocorrelation function of (a) root zone soil moisture anomalies and (b) precipitation anomalies; (c) annual cycle of precipitation–root zone soil moisture cross correlation. In (c), positive lags refer to precipitation lagging soil moisture (i.e., soil moisture leading precipitation) and negative lags refer to precipitation leading soil moisture. For example, the location (4, DJF) indicates the correlation of DJF root zone soil moisture anomaly with the precipitation anomaly the following AMJ (i.e., 4 months later), while the location (−6, MJJ) indicates the correlation of MJJ root zone soil moisture anomaly with the precipitation anomaly the previous NDJ (i.e., 6 months earlier). (d)–(g) Cross correlation between the root zone soil moisture anomaly [in (d) DJF, (e) MAM, (f) JJA, and (g) SON] and the soil moisture anomaly as a function of depth and lead/lags. For example, in the SON panel the location (5, −0.5) indicates the correlation of SON root zone soil moisture anomaly with the soil moisture anomaly at depth 0.5 m in the following year FMA season (i.e., 5 months later); the location (−5, −0.8) in the DJF panel indicates the correlation of DJF root zone soil moisture anomaly with the soil moisture anomaly at depth 0.8 m in the previous year’s JAS season (i.e., 5 months earlier).

  • View in gallery

    As in Fig. 8, but for the GP time series.

  • View in gallery

    Annual cycle of root zone soil moisture anomaly autocorrelation function for the SW time series, in LDAS datasets. All figures represent results from 1980 to 2010, except for the top row center, which shows 1950–2010. Results for the ensemble mean for 1980–2010 are shown in the second row left corner.

  • View in gallery

    As in Fig. 10, but showing the annual cycle of root zone soil moisture anomaly autocorrelation function for the GP time series, in the LDAS datasets. All figures represent results from 1980 to 2010, except for the top row center, which shows 1950–2010. Results for the ensemble mean for 1980–2010 are shown in the second row left corner.

  • View in gallery

    Annual cycle of root zone soil moisture autocorrelation function for Illinois from all soil moisture dataset (cf. Table 1). Ensemble mean results include all soil datasets shown here except for the subsampled version of the VIC-highres.

  • View in gallery

    Annual cycle of root zone soil moisture autocorrelation for selected in situ sites (see text for more details, and Fig. A2 for site locations).

  • View in gallery

    Annual cycle of top 1-m soil moisture autocorrelation for the SW time series, from different VIC-lowres datasets based on (a) observed forcing (cf. Fig. 11), (b) observed temperature and climatological precipitation forcing (“precip climo”), and (c) climatological temperature and observed precipitation forcing (“temp climo”), for the years 1950–2010. (d) The corresponding analysis applied to the same region and period in the CPC (“leaky bucket”) dataset. Note that unlike previous figures, these results are for the 0–1-m soil layer, except for CPC, which represents 0–1.6 m.

  • View in gallery

    As in Fig. 14, but showing the annual cycle of top 1-m soil moisture autocorrelation for the GP time series, from different VIC-lowres datasets based on (a) observed forcing (cf. Fig. 12), (b) observed temperature and climatological precipitation forcing (“precip climo”), and (c) climatological temperature and observed precipitation forcing (“temp climo”), for the years 1950–2010. (d) The corresponding analysis applied to the same region and period in the CPC (“leaky bucket”) dataset.

  • View in gallery

    Locations of station data and the boundaries for the three regional indexes used in this study.

  • View in gallery

    Correlation of ICN mean root zone soil moisture anomaly with corresponding anomaly from each soil moisture dataset averaged within Illinois, as a function of season for the years 1985–2004. Note that the CPC dataset represents soil moisture in the 0–1.6-m layer. Ensemble mean results here include all datasets except CPC, and the subsampled version of the VIC-highres. Three instances of VIC are included to illustrate differences in model scale configuration, as well as the importance of subsampling daily model outputs on the sampling dates and location of the ICN stations.

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Potential Reemergence of Seasonal Soil Moisture Anomalies in North America

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  • 1 School of Forestry and Wildlife Sciences, Auburn University, Auburn, Alabama
  • | 2 Cooperative Institute for Research in Environmental Sciences, University of Colorado Boulder, and Physical Sciences Division, NOAA/Earth System Research Laboratory, Boulder, Colorado
  • | 3 Cooperative Institute for Research in Environmental Sciences, and Department of Civil, Environmental, and Architectural Engineering, University of Colorado Boulder, Boulder, Colorado
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Abstract

Soil moisture anomalies within the root zone (roughly, soil depths down to ~0.4 m) typically persist only a few months. Consequently, land surface–related climate predictability research has often focused on subseasonal to seasonal time scales. However, in this study of multidecadal in situ datasets and land data assimilation products, we find that root zone soil moisture anomalies can recur several or more seasons after they were initiated, indicating potential interannual predictability. Lead–lag correlations show that this recurrence often happens during one fixed season and also seems related to the greater memory of soil moisture anomalies within the layer beneath the root zone, with memory on the order of several months to over a year. That is, in some seasons, notably spring and summer when the vertical soil water potential gradient reverses sign throughout much of North America, deeper soil moisture anomalies appear to return to the surface, thereby restoring an earlier root zone anomaly that had decayed. We call this process “reemergence,” in analogy with a similar seasonally varying process (with different underlying physics) providing winter-to-winter memory to the extratropical ocean surface layer. Pronounced spatial and seasonal dependence of soil moisture reemergence is found that is frequently, but not always, robust across datasets. Also, some of its aspects appear sensitive to spatial and temporal sampling, especially within the shorter available in situ datasets, and to precipitation variability. Like its namesake, soil moisture reemergence may enhance interannual-to-decadal variability, notably of droughts. Its detailed physics and role within the climate system, however, remain to be understood.

Denotes content that is immediately available upon publication as open access.

Supplemental information related to this paper is available at the Journals Online website: https://doi.org/10.1175/JCLI-D-18-0540.s1.

© 2019 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Sanjiv Kumar, szk0139@auburn.edu

Abstract

Soil moisture anomalies within the root zone (roughly, soil depths down to ~0.4 m) typically persist only a few months. Consequently, land surface–related climate predictability research has often focused on subseasonal to seasonal time scales. However, in this study of multidecadal in situ datasets and land data assimilation products, we find that root zone soil moisture anomalies can recur several or more seasons after they were initiated, indicating potential interannual predictability. Lead–lag correlations show that this recurrence often happens during one fixed season and also seems related to the greater memory of soil moisture anomalies within the layer beneath the root zone, with memory on the order of several months to over a year. That is, in some seasons, notably spring and summer when the vertical soil water potential gradient reverses sign throughout much of North America, deeper soil moisture anomalies appear to return to the surface, thereby restoring an earlier root zone anomaly that had decayed. We call this process “reemergence,” in analogy with a similar seasonally varying process (with different underlying physics) providing winter-to-winter memory to the extratropical ocean surface layer. Pronounced spatial and seasonal dependence of soil moisture reemergence is found that is frequently, but not always, robust across datasets. Also, some of its aspects appear sensitive to spatial and temporal sampling, especially within the shorter available in situ datasets, and to precipitation variability. Like its namesake, soil moisture reemergence may enhance interannual-to-decadal variability, notably of droughts. Its detailed physics and role within the climate system, however, remain to be understood.

Denotes content that is immediately available upon publication as open access.

Supplemental information related to this paper is available at the Journals Online website: https://doi.org/10.1175/JCLI-D-18-0540.s1.

© 2019 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Sanjiv Kumar, szk0139@auburn.edu

1. Introduction

Long-term (multiyear) droughts occur worldwide, particularly in semiarid to arid regions such as the southwestern United States, the Sahel, and Australia (Cheng et al. 2016; Evans et al. 2017; Held et al. 2005). In North America, the recent California drought (2012–15) resulted in billions of dollars of economic losses and severe stress on ecosystem productivity (Asner et al. 2016; Howitt et al. 2015). Over the past century the U.S. Great Plains has experienced both costly droughts and extended pluvial periods (Livneh and Hoerling 2016). Improved understanding of mechanisms behind the potential predictability of long-term phenomena mediated by the land surface, including drought, may better inform natural resource planning decisions.

Drought is triggered by a substantial precipitation deficit that can even develop in a matter of days to weeks (Hoerling et al. 2014; Mo and Lettenmaier 2015), with surface feedbacks including antecedent conditions subsequently intensifying and prolonging the resulting soil moisture deficit (Lyon and Dole 1995; Oglesby and Erickson 1989; Otkin et al. 2016; PaiMazumder and Done 2016). Soil moisture and precipitation feedbacks in the Great Plains are asymmetric, with droughts driving higher precipitation variability than floods (Schubert et al. 2008). More generally, since soil moisture anomalies persist longer than atmospheric moisture anomalies, land processes contribute to both subseasonal (Koster et al. 2010, 2011) and seasonal (Guo et al. 2011; Kumar et al. 2014b; Paolino et al. 2012) climate predictability. Realistic soil moisture initializations also improve seasonal streamflow and soil moisture forecasts (Orth and Seneviratne 2013), because of time-integration effects of soil moisture and snow processes at watershed scales (Wood et al. 2016).

“Soil moisture memory” refers to the degree of persistence (high memory) or dissipation (low memory) of a soil moisture anomaly through time (Koster and Suarez 2001). Numerous studies have found that memory in the surface soil ranges between about 2 and 4 months, both in observations (Amenu et al. 2005; Dirmeyer et al. 2016; Entin et al. 2000; Nicolai-Shaw et al. 2016; Orth and Seneviratne 2012; Vinnikov et al. 1996; Wu et al. 2002) and climate model simulations (Delworth and Manabe 1988; Koster and Suarez 2001; Seneviratne and Koster 2012; Seneviratne et al. 2006; Wu and Dickinson 2004). Theoretical estimates from soil water balance models yield similar values (Ghannam et al. 2016; Orth et al. 2013; Seneviratne and Koster 2012). This memory time scale is spatially dependent, and dry regions may have higher memory (~3 months) than wet regions (~1 month) (Rahman et al. 2015).

However, if surface soil moisture memory is on the order of months, then what accounts for long-term droughts and pluvials persisting beyond a season, even years, seen in both instrumental and paleo-proxy climate datasets and in model simulations (Ault et al. 2013; Cook et al. 2016; Cook et al. 2004; Herweijer et al. 2007; Kam and Sheffield 2016; Langford et al. 2014; Schubert et al. 2004; Seager et al. 2005; Wu and Kinter 2009)? One explanation is that atmospheric teleconnections from ocean basins (Hoerling et al. 2014; Nicolai Shaw et al. 2016; Routson et al. 2016; Wu and Kinter 2009), including the tropical Pacific (Cole et al. 2002; Hoerling and Kumar 2003; Schubert et al. 2008; Seager et al. 2005) and the extratropical Atlantic (McCabe et al. 2004; Schubert et al. 2004), drive long-term variations in precipitation. Even without oceanic forcing, extended periods with substantial precipitation anomalies could occur randomly through natural variations of weather alone (Hasselmann 1976; Langford et al. 2014; Stevenson et al. 2015) despite its generally short memory (Chikamoto et al. 2015; Schubert et al. 2016; Seager et al. 2015). While historical “megadroughts” (Woodhouse and Overpeck 1998) may additionally be forced by changes in volcanism and solar insolation (Seager et al. 2007; Woodhouse and Overpeck 1998), they too likely reflect internal climate variability (Ault et al. 2018; Coats et al. 2016; Seager et al. 2007, 2008).

Even so, observational and model studies have consistently identified multiseasonal to multiyear memory in deep soil moisture and groundwater, which could also contribute to long-term climate predictability including drought (Amenu et al. 2005; Bellucci et al. 2015; Bierkens and van den Hurk 2007; Entekhabi et al. 1996; Xia et al. 2014) and pluvials (Schubert et al. 2008). For example, the memory time scale of Illinois soil moisture anomalies below about 1-m depth is close to a year (Amenu et al. 2005). Soil moisture stored in the wet season supports plant growth in the subsequent dry season (Huete et al. 2006; Markewitz et al. 2010; Yan and Dickinson 2014). Groundwater might impact evapotranspiration through upward soil water flux (Fan and Miguez-Macho 2010; Miguez-Macho and Fan 2012) so recycling of evaporative flux could contribute to multiyear persistence in rainfall anomalies (Bierkens and van den Hurk 2007). Mahanama et al. (2012) found that 1 October initialization of soil moisture contributes to skill in streamflow forecasts at longer lead times, such as the following spring and summer seasons. Schubert et al. (2004) suggested that Great Plains drought is partly a consequence of year-to year “deep” soil memory. Analyses of megadroughts have also suggested that land surface memory must significantly contribute to their persistence (Ault et al. 2018; Cook et al. 2016). These studies all suggest that land surface memory is effectively greater than just a few months.

What seems to have received less attention is just how longer memory within the deep layer is communicated to the shorter-memory surface layer to sustain climate anomalies like long-term drought. Figure 1 both illustrates this issue and a potential explanation, showing a vertical cross section of the evolution of anomalous soil moisture during the 1988–89 Illinois drought, based on Illinois Climate Network (ICN) in situ data (Hollinger and Isard 1994). The spring 1988 precipitation deficit induced a dry surface soil moisture anomaly that propagated downward during summer 1988. While anomalies to a depth of ~40 cm decayed over a few months, as expected, beneath this depth the dry anomaly persisted throughout the following winter and spring. In spring 1989, even though precipitation was slightly above normal, surface soil moisture anomalies again became more negative. Interestingly, only afterward, in April, did a negative precipitation anomaly develop. Could the deep soil moisture anomaly have had any role in these surface changes, such as by driving anomalously dry surface soil conditions to recur in the second year?

Fig. 1.
Fig. 1.

Evolution of Illinois soil moisture standardized anomalies during and after the 1988 drought, averaged over Illinois Climate Network (ICN) observations. Contour interval is 0.25 standard deviation. Also shown are the standardized precipitation anomalies (bars) for each month.

Citation: Journal of Climate 32, 10; 10.1175/JCLI-D-18-0540.1

This example is reflected in the overall ICN statistics. Figure 2a shows the autocorrelation function of Illinois springtime root zone soil moisture seasonal anomalies for 1985–2004. Here and in the remainder of this paper, we define the “root zone” as spanning depths of 0–0.4 m, the soil layer where typically two-thirds or more of the plant roots reside and also the layer with the highest seasonal variability (Ghannam et al. 2016; Zeng 2001). The details of the calculation are deferred to section 3; they are not necessary to grasp the main point here. As expected from a first-order Markov process, the autocorrelation function initially decays exponentially toward zero, with an e-folding time scale of about 4 months, consistent with previous studies discussed above. However, for longer lags the autocorrelation does not remain near zero but instead increases to become significantly positive again for leads of 13–15 months. That is, even as Illinois anomalous root zone soil moisture was uncorrelated from spring to the subsequent fall, it was significantly correlated from one spring to the next.

Fig. 2.
Fig. 2.

Autocorrelation function of anomalous Illinois root zone (0–0.4-m depth) soil moisture and precipitation. Indices are determined from statewide averages of Illinois Climate Network (ICN) observations for 1985 to 2004, as described in the text. Anomalies are departures from the monthly seasonal cycle, smoothed with a 3-month running mean. (a),(b) Autocorrelation of springtime root zone soil moisture and precipitation, respectively. In both panels, autocorrelation lag is measured from the base FMA (February–April) anomalies; so, for example, a lead of 6 months represents the correlation between FMA and the subsequent ASO season. Dashed blue lines show the observed autocorrelation functions; solid black lines show exponential decay, where the decorrelation (e-folding) time scale is determined from a fit to the entire autocorrelation function. The red dots indicate values that are significantly different (95% confidence interval; see section 3c) from zero. (c),(d) Annual cycle of the autocorrelation function for 3-month running mean root zone soil moisture and precipitation anomalies, respectively. The month ordinate indicates the time of the base season, and the abscissa shows the lead/lag. For example, the (−13, MAM) value in (c) indicates the correlation of MAM root zone soil moisture anomaly with the previous year’s FMA root zone soil moisture anomaly (i.e., 13 months earlier); the (14, FMA) value (magenta oval) indicates the correlation of FMA root zone soil moisture anomaly with the root zone soil moisture anomaly in the next year’s AMJ season (i.e., 14 months later). The diagonal yellow lines therefore represent correlations with the previous FMA (subsequent AMJ) seasons, for any lead/lag. Correlation maxima along these lines are suggestive of reemergence. Note that both magenta ovals represent the 14-month lag correlation between FMA and the following AMJ (one oval forward and the other backward). The horizontal black dashed lines represent the location of the values in the blue dashed lines in (a) and (b). Note that in this and all subsequent plots, vertical dashed gray lines are drawn at 6-month intervals, and stippling represents the 95% confidence interval.

Citation: Journal of Climate 32, 10; 10.1175/JCLI-D-18-0540.1

In fact, the annual cycle of the autocorrelation function (Fig. 2c) shows that while root zone soil moisture anomalies initially last only a few months, they recur in the subsequent spring (diagonal line), no matter the base season of the autocorrelation function. Yet no significant recurrence is apparent for precipitation (Figs. 2b and 2d). Together with Fig. 1, these results suggest that some springtime process might have partially restored prior soil moisture anomalies within the root zone by bringing back the memory of the previous year stored in the soil layer below. We call such a seasonally dependent process soil moisture reemergence, in analogy with a similar seasonally varying process (albeit with different underlying physics) that provides long-term memory to thermal anomalies within the surface layer of the extratropical oceans (Alexander and Deser 1995; Alexander et al. 1999; Deser et al. 2003) and appears responsible for a substantial fraction of the variance of the Pacific decadal oscillation (PDO; Mantua et al. 1997; Newman et al. 2016).

Our immediate aim in this paper is to begin developing the following soil moisture reemergence hypothesis: deep layer soil moisture acts as a memory reservoir with significantly greater memory, ranging from several months to a year or longer (Amenu and Kumar 2008), than is typically present either in the root zone or in daily weather. Deep anomalies can interact with root zone soil moisture. If this interaction exists year-round, it may be expected to generally lengthen root zone memory time scales. However, when the connection is mediated by seasonally varying processes such as changes in snow cover, vegetation, and land–atmosphere coupling, then the root zone memory will generally be shorter except during seasons when the interaction with the deeper layer is pronounced, leading to soil moisture reemergence.

We would like to start by investigating how observations may constrain the proposed reemergence process and its possible physical mechanisms, examining the seasonal, regional, and depth dependence of soil moisture memory and its relationship to precipitation. This means going beyond earlier analyses of soil moisture memory, by determining the autocorrelation function of anomalous soil moisture over time intervals as long as two years. Unfortunately, the long-term, in situ soil moisture observations needed to study this phenomenon are limited. Therefore, much of this study involves evaluating long-term soil moisture memory and potential reemergence in various land data assimilation products. These products have their own well-known limitations, since they are derived from observed atmospheric forcing of the current generation of land surface models, but they yield results that appear reasonable on large scales (Dirmeyer et al. 2016). Since it is important to put the statistical analysis in a physical context, we first briefly introduce some potential mechanisms in section 2. Then, after summarizing all available soil moisture “datasets” that we analyze in section 3, the results of our analysis are presented in section 4. Finally, section 5 presents a summary and evaluation of our findings, including noting limitations of using datasets that are largely model-based and suggesting some avenues for further investigation.

2. Hypothesized soil moisture reemergence mechanisms

We first present some potential soil moisture reemergence mechanisms, in the context of the conceptual two-layer soil system model (Fig. 3):
e1
e2
where S1 and S2 are root zone (0–0.4 m) and deep layer (0.4–2 m) soil moisture, respectively. Here, we restrict our “deep layer” definition to only 2-m depth because this is where observations and data are readily available, but clearly soil and the water table below this depth may be relevant. Also, P is precipitation, ET is evapotranspiration, SR is surface runoff, and D is base flow and drainage; T represents coupling between the root zone and deep soil layers, defined to be positive when water flows from the deep soil to the root zone.
Fig. 3.
Fig. 3.

A conceptual two-layer soil moisture model; see text for more details.

Citation: Journal of Climate 32, 10; 10.1175/JCLI-D-18-0540.1

Darcy’s law [(3)] governs water movement within a soil–plant–atmosphere continuous system as water moves from high to low potential (Goldsmith 2013):
e3
where is the rate of water flow (m s−1) in the soil system, K is hydraulic conductivity (m s−1), and is change in total soil water potential per unit length; for example, for water movement in the soil system. Figure 4a shows the soil moisture climatology and interannual variability from ICN data. The corresponding soil water potential in Illinois shows a reversal from high to low potential between the root zone and deep layer in the late spring and summer seasons (see Fig. S1 in the online supplemental material).
Fig. 4.
Fig. 4.

Physics of soil moisture reemergence: a demand-driven hypothesis. (a) Soil moisture climatology, variability, and (P − ET)/P* climatology: color shading shows monthly climatology of soil moisture in terms of percentage of saturation as a function of depth from the surface to 2 m. Line contours represent interannual variability using an estimate of one standard deviation from the ICN data. Bars shows P − ET climatology, normalized by annual average precipitation, using LDAS data from CLM. (b) An estimate of two major components: (P − ET − SR) and T, based on data from CLM. Error bars show interannual variability using an estimate of one standard deviation. Note the major contribution of T in the summer season. Units are mm month−1. P* is annual average precipitation.

Citation: Journal of Climate 32, 10; 10.1175/JCLI-D-18-0540.1

It is widely accepted that water can move upward from the deep layer to the root zone following a soil water (matric) potential gradient (Green and Ampt 1911), which could occur when mean evapotranspiration exceeds precipitation in the growing season (Huete et al. 2006; Kumar and Merwade 2011; Kumar et al. 2014a; Markewitz et al. 2010; Sheffield et al. 2013; Yan and Dickinson 2014); that is, ET − P deficits are supplied by the soil moisture storage available from previous seasons. Upward moisture fluxes on the basis of soil moisture gradients have been observed in nature (Scanlon 1992) and corroborated by models (Scanlon and Milly 1994), although these types of assessments have not been done over long periods or large areas. Examples of physical mechanisms that might drive water upward include 1) hydraulic redistribution, which is water movement from deep wet soil to dry shallow soil through the root system in the absence of transpiration demand (Lee et al. 2005; Meinzer et al. 2004; Neumann and Cardon 2012; Ryel et al. 2003; Ryel et al. 2002); 2) deep root plant water uptake, where deeper-rooted plants can access deep layer (and therefore higher memory) soil water (Huete et al. 2006); and 3) a shallow groundwater table position, which can contribute to the evaporative demand through capillary rise especially during droughts (Gao et al. 2017; Rizzo et al. 2018).

Figure 4b shows the climatology of various terms in (1) from an offline land surface model simulation (CLM, discussed later), which suggests that T constitutes a major portion (brown shading) of P − ET − SR deficits in the summer, as well as contributing to the recharge of deep soil moisture during winter and early spring. Importantly, there are no direct observations of T; rather, it can be inferred as a difference term between soil moisture observations at two depths. Given a lack of long-term, high-quality observations needed for T (ICN notwithstanding), we must rely almost entirely on simulated soil moisture, which introduces uncertainty in the magnitude of potential reemergence.

A “demand-driven” soil moisture anomaly reemergence hypothesis might then act as follows: the root zone soil moisture anomalies contribute to deep layer anomalies during the wet season when the atmospheric supply exceeds the demand; that is, P − ET > 0. The deep layer anomalies remain decoupled from atmospheric/evapotranspiration processes during winter and early spring because atmospheric demand is smaller than the atmospheric supply. As a result, the deep layer soil moisture has greater memory and smaller variability compared to the root zone (Fig. 4a). As the surface soil moisture dries out in late spring and summer, the soil water potential gradient reverses (i.e., the deep layers have higher soil water potential than the surface), leading to moisture transfer from the deep layer to the root zone.

It is also possible that reemergence can occur without upward water movement. This alternative “anomaly-propagation” hypothesis is illustrated in Fig. 5. Consider first the case of a pre-existing wet deep layer anomaly (left column). During the subsequent season, the rate of downward water transfer to the deep layer would be reduced (i.e., there would be a negative T anomaly) because of a smaller-than-normal matric potential gradient between the root zone and deep layers. This would result in a net positive root zone soil moisture anomaly and an apparent upward propagation of the prior deep layer anomaly. Conversely, a dry deep layer anomaly would imply a larger-than-normal matric potential gradient between the root zone and deep layers, a positive T anomaly, and again apparent upward propagation of the deep layer anomaly (right column in Fig. 5b).

Fig. 5.
Fig. 5.

Physics of soil moisture reemergence: anomaly propagation hypothesis. Both panels depict the conceptual two-layer soil model of Fig. 3, with anomalous soil moisture conditions and the total soil water potential (soil matric potential and gravitational potential with reference at 2-m depth) with anomalous soil moisture in the deep layer and (without loss of generality) climatological conditions in the root zone. (a) A deep layer wet anomaly would lead to a smaller potential gradient between the root zone and the deep layer and consequently a reduced magnitude of T, resulting in a wet anomaly developing in the root zone. (b) A deep layer dry anomaly would lead to larger potential gradient between the root zone and the deep layer and consequently an increased magnitude of T, resulting in a dry anomaly developing in the root zone. Numbers in the parentheses (X ± Y) show the total soil water potential (meters of water) using ICN data for FMA season, where X represents the climatological mean value and Y represents one standard deviation of interannual variability. The hatched horizontal arrow in the deep layer represents the transfer of memory from the previous season to the current season. Filled thick black arrows show total water movement from root zone to the deep layer below. Filled thick red arrows show the drainage term. See text for further explanation.

Citation: Journal of Climate 32, 10; 10.1175/JCLI-D-18-0540.1

Clearly, both the proposed demand-driven and anomaly-propagation hypotheses are quite sensitive to how T depends upon all the other terms in (1), so the root zone anomaly development is likely considerably more complex than discussed here and may act differently in the presence of climate variability, surface heterogeneity, and land–atmosphere coupling. This two-layer heuristic model also oversimplifies the more complicated water movement through the soil column, including interactions with the aquifer below as well as lateral flow. How vegetation, both through its seasonal cycle of growth and sensitivity to soil moisture anomalies, impacts these mechanisms is also likely important. Still, fundamental physics (the Darcy law) and the observed matric potential gradients together provide possible mechanistic explanations for soil moisture reemergence.

Finally, K. Schaefer et al. (2007) suggested that freeze–thaw processes can lead to soil temperature reemergence in cold regions: during the winter, soil temperature anomalies from the previous season are stored below the frozen surface, and then reappear at the surface during the subsequent thaw (also see Matsumura and Yamazaki 2012). A similar mechanism (perhaps also involving snowpack dynamics) might be relevant for moisture anomalies as well.

3. Data and methods

a. Soil moisture datasets and processing

Table 1 lists all the hydrology/land surface model datasets and in situ soil moisture measurements (and their acronyms) used in this study, including their period of record and their horizontal resolution. Below, we briefly describe these datasets. Given the short records of in situ and satellite soil moisture datasets, our methodology is limited to providing essentially a qualitative assessment of the “potential” existence of a reemergence phenomenon and its attributes, rather than a quantitative assessment of its magnitude. In this context, we focus on several multilayer soil moisture Land Data Assimilation System (LDAS) datasets that include different land surface models (LSMs) driven by observed meteorological forcing. This provides the longer records needed to study interannual to decadal variability. Note that LDAS datasets do not directly assimilate soil moisture observations, however. Another important caveat is that the phenomenon of reemergence has not been directly built in to any of the models, nor has it been explicitly evaluated before, such that some models may be more or less suitable to simulate reemergence and that any characterization of reemergence from these models is likely to contain artifacts related to parameterization and discretization dependences.

Table 1.

Datasets used in this paper. Note that some datasets cover more years than were used.

Table 1.

We examined three LDAS methods with at least 60 years of data each. First, we used the Variable Infiltration Capacity model (VIC; Liang et al. 1994) in two configurations: 1) a hydrologically consistent high-resolution (1/16°) implementation, called VIC-highres, calibrated to streamflow observations (Livneh et al. 2013) and therefore providing an observationally constrained representation of soil moisture interactions relative to other model datasets; and 2) a lower-resolution (1/2°), spatially uniform soil depth implementation of VIC, called VIC-lowres, used by Livneh and Hoerling (2016) to simulate drought at scales comparable to GCMs, providing a useful contrast to the VIC-highres concerning model spatial resolution and calibration effects. Both use a three-layer soil moisture scheme, but VIC-highres uses spatially varying thicknesses dependent on its streamflow calibrations. Both are driven by gridded meteorological forcing data from approximately 20 000 NOAA Cooperative Observer stations (Livneh et al. 2013, 2015b), and both include a seasonally varying vegetation phenology and resolve both water and energy fluxes for the land surface and vegetation canopy layers. Additional experiments were made with the VIC-lowres in which the forcing is modified by fixing either precipitation or temperature to their climatologies (Livneh and Hoerling 2016) to explore the sensitivity of our results to anomalous meteorological forcing.

The VIC is contrasted with the Community Land Model version 4.5 (CLM; (Oleson et al. 2013), an LSM with more sophisticated soil–plant–atmosphere interaction. The CLM has a coarser (1° × 1°) spatial resolution but also has a 10-layer fixed depth soil moisture scheme down to 3.5-m depth. It solves the one-dimensional Richard’s equation within each soil column, which can share several plant functional types to account for vegetation heterogeneity at the surface. Plant functional types describe vegetation structure in terms of leaf properties, canopy heights, and root distributions (Bonan et al. 2002; Oleson et al. 2013). CLM also has a prognostic seasonal cycle of vegetation evolution, emergence and senescence of leaves, and vegetation heights based on the Biome-biogeochemical cycle model (Thornton and Rosenbloom 2005; Thornton et al. 2002). The soil moisture dataset is then generated by forcing the CLM with meteorological observations based on the Climatic Research Unit (CRU)–National Centers for Environmental Prediction (NCEP) dataset, for the years 1901–2010. Despite differences between VIC and CLM, they produce similar snowpack dynamics (Chen et al. 2014) and share common physics assumptions: a two-stream canopy radiative transfer scheme, time-varying albedo, liquid water refreeze, and water transfer between snow layers.

Sensitivity to LDAS models is explored by analysis of two datasets from phase two of the North American Land Data Assimilation System (NLDAS-2) (Xia et al. 2012, 2014) based on the Noah and Mosaic models, covering the period since 1979. The Noah model has four soil layers with thicknesses of 10, 30, 60, and 100 cm. It provides land boundary conditions in the NOAA/NCEP coupled Climate Forecast System (Ek et al. 2003). Mosaic has three soil layers with thicknesses of 10, 30, and 160 cm, with the first two together comprising the root zone (Koster and Suarez 1996). Since both models receive identical observed atmospheric forcing, differences between these two datasets arise from model differences including their soil moisture parameterizations. We also examined the NLDAS-2 dataset based on the VIC model, but show the results obtained with the VIC-highres dataset instead since the differences have relatively minor impact on our results, and VIC-highres covers a longer period.

To provide a simplistic LSM for comparison, we used the Climate Prediction Center (CPC) soil moisture dataset, which uses observations to force a single-layer “leaky bucket model” (Huang et al. 1996; van den Dool et al. 2003) with an effective depth of 1.6 m. In essence, we have incorporated soil moisture datasets from a wide range of model parameterizations, from the most simplified with no vertical layers to complex (interactive vegetation phenology; CLM) and hydrologically calibrated (VIC) models.

More recently, remote sensing–based surface soil moisture observations have been assimilated to produce daily root zone soil moisture values at higher spatial resolution for the 1980–2015 period. Two such products are 1) the Global Land Evaporation Amsterdam Model (GLEAM), which assimilates soil moisture observations from different passive and active C- and L-band microwave sensors from European Space Agency Climate Change Initiative (ESA-CCI), using a three-layer water balance model where root zone depth is a function of land cover type; and 2) SoilMERGE (SMERGE), which was developed based on merging an NLDAS land surface model (Noah) dataset with the ESA-CCI satellite retrievals (Crow and Tobin 2018), using an exponential filter to convert surface soil moisture (0–5 cm) to root zone soil moisture (0–40 cm) (Tobin et al. 2017). In addition, we included the Modern-Era Retrospective Analysis for Research and Applications version 2 (MERRA-2; Gelaro et al. 2017), a reanalysis product using observed precipitation to force the coupled land–atmosphere system, allowing near-surface temperature and humidity to be consistent with the precipitation correction and providing comparable performance to the corresponding LDAS-type simulations (Reichle et al. 2017). Finally, we determined an ensemble mean from all the above datasets for the common 1980–2010 period.

Given LSM/LDAS limitations, we might prefer to focus on in situ measurements, but such records are generally not over ~20 years in length, and most are shorter (Dirmeyer et al. 2016). The ICN covers 18 sites in Illinois from 1983 to 2004 (Hollinger and Isard 1994). Measurements were taken from 11 soil layers at depths of 0–10, 10–30, 30–50, 50–70, 70–90, 90–110, 110–130, 130–150, 150–170, 170–190, and 190–200 cm, generally once per month during the nongrowing season and twice per month (or more, in a few locations) during the growing season. Comparing LDAS and ICN datasets (see appendix A) shows that the VIC-highres best matched ICN, but that sparse ICN temporal sampling impacts our analysis.

Finally, we constructed monthly averages of daily soil moisture observations from sites that had at least 12 years of continuous monthly mean data to a depth of 40 cm. These include Ashton (ARM) in Kansas, Mandan (SCAN) in North Dakota, Adam’s Ranch (SCAN) in New Mexico, Happy Jack (SNOTEL) in Arizona, Long Valley (SNOTEL) in Idaho, and Reynold’s Creek (SNOTEL) in Idaho (see appendix A for more details, and Fig. A2 for their locations) (Bond 2005; Schaefer and Paetzold 2001; G. Schaefer et al. 2007). All in situ soil moisture observations were obtained from the International Soil Moisture Network (Dorigo et al. 2011, 2013).

b. Determining soil moisture seasonal anomalies

For each dataset, we smoothed the monthly averages with a 3-month running mean; this reduces intraseasonal variability but does not affect our results, as is illustrated in Fig. S2. We then computed the 3-month running mean anomalies by removing the long-term monthly climatology determined from the period of record. We tested the impact of linearly detrending the 1950–2010 datasets separately for each month but found the effects were small. Also, the trend since 1950 has both anthropogenic and natural sources (Solomon et al. 2011), and identification of only the external component is beyond the scope of this paper. Consequently, all analyses shown are based on data that were not detrended.

To focus on larger spatial scales, time series were computed by area averaging data within the boxes shown in Fig. 6 (see also Fig. A1), representing four regions: Illinois (also see appendix A), the Great Plains (GP), the Great Basin (GB), and the southwestern United States (SW).

Fig. 6.
Fig. 6.

(top) Root zone soil moisture standard deviation and (lower rows) lag correlation from 3 to 18 months, for MAM base season, 1950–2010, in the (left) NCAR CLM and (right) VIC-highres datasets. Only statistically significant autocorrelations (95% level) are shown using color scale in rows 2–7. Numbers in each panel show the percent of areal coverage of the significant autocorrelations. The outlines of boxes used to define the regional time series (see text and also Fig. A2) are also shown.

Citation: Journal of Climate 32, 10; 10.1175/JCLI-D-18-0540.1

c. Metrics

Most of the analysis in this paper involves the annual cycle of correlation functions for soil moisture and precipitation, determined separately for each 3-month season by correlating that season’s anomalies with values at lags ranging from −24 to +24 months. These correlations were found both for a variable with itself [autocorrelation (AC)] and between two different variables [cross-correlation (CC)].

For comparison, note that the land surface integrates forcing by random weather and climate variability. Therefore, the simplest null hypothesis for soil moisture variability is red noise or a first-order Markov process (Amenu et al. 2005; Chikamoto et al. 2015; Delworth and Manabe 1988; Schlosser and Milly 2002), whose autocorrelation function ρ for a given lag τ is
e4
where τD is the decorrelation (or e-folding) time scale, also known as soil moisture memory. See appendix B for more details of the AC and CC calculations and their significance testing.

To develop a measure for evaluating reemergence, we first recall that the autocorrelation function in Fig. 2a declined from one to near zero but then increased at longer lags, reaching a maximum of 0.65 at a 14-month lag. This behavior can be captured by defining the recurrence time scale TR as the lag at which the autocorrelation function reaches its first secondary maximum (i.e., 14 months in Fig. 2a). Note that TR is only evaluated when the correlation value at this secondary maximum (or the recurrence magnitude) is statistically significant at the 95% level (appendix B), Importantly, TR is a function of the starting season; that is, it measures how long it takes until an anomaly from a given season will recur. So, from Fig. 2b, for example, FMA soil moisture anomalies recur after about TR = 14 months [in the second year April–June (AMJ) season], whereas AMJ soil moisture anomalies take TR = 12 months to recur (also in AMJ). Since no information about subsurface soil moisture anomalies is used to compute TR, we call it a measure of anomaly recurrence, not (necessarily) reemergence.

4. Results

a. Soil moisture memory and reemergence in North America

Figure 6 shows maps of springtime [March–May (MAM)] root zone soil moisture anomaly amplitude (i.e., standard deviation) for the CLM and VIC-highres datasets. [Fig. S3 shows results for the other three seasons.] Qualitatively similar large-scale features exist in both datasets, including pronounced maxima extending along a north–south direction through the Great Plains and in the southeast. However, clear differences in detail exist; for example, CLM variability is stronger in the northern Great Plains whereas VIC-highres variability is stronger in the Great Basin. These differences do not merely reflect the higher resolution effects (VIC-highres) but can result from differences in forcing, model structure, and soil moisture parameterizations.

Interestingly, the largest anomalies are not always the most persistent, as shown by the autocorrelation function maps for correlations between MAM anomalies and anomalies 3 [June–August (JJA)], 6 [September–November (SON)], 9 [December–February (DJF)], 12 (MAM +1), 15 (JJA +1), and 18 (SON +1) months later (Fig. 6). For example, at 3-month lead, there is substantially greater memory in the Great Basin and the Southeast and less in the Great Plains and southwestern United States. Despite this, at 9-month lead the Great Basin and Great Plains autocorrelation values are similar; in fact, the 9-month lead Great Plains autocorrelation increases considerably from its minimum at 6-month lead (cf. Fig. 2a). Likewise, the Southwest U.S. autocorrelation function reaches a secondary maximum at 18-month lead. Similar results are apparent in maps of autocorrelation functions lagged from JJA and SON anomalies (see Figs. S3a–c) except that these secondary maxima occur at different leads.

Note that these maps are field significant at all lags; that is, at least 5% of each map contains locally significant correlation at the 95% threshold. However, at some lags this is due to some statistically significant negative correlations, which could reflect precipitation forcing and not necessarily (at least not obviously) land effects.

To evaluate the potential for reemergence, we determined TR (section 3c) from the CLM and VIC-highres datasets. The resulting maps (Fig. 7), based on the DJF, MAM, JJA, and SON seasons, have greater coverage than in Fig. 6 for the same significance value, which suggests that there is some uncertainty in the precise time scale of recurrence.

Fig. 7.
Fig. 7.

Recurrence time scale TR for root zone anomalous soil moisture in DJF, MAM, JJA, and SON base seasons, 1950–2010. Only values of TR for which the recurrence magnitude is significant at the 95% level are shown. (left) TR maps determined from CLM data for (a) DJF, (b) MAM, (c) JJA, and (d) SON. (right) As in left, but for VIC-highres for (e) DJF, (f) MAM, (g) JJA, and (h) SON. The outlines of boxes used to define the regional time series are also shown.

Citation: Journal of Climate 32, 10; 10.1175/JCLI-D-18-0540.1

Overall, recurrence of root zone soil moisture anomalies is widespread throughout North America, albeit more pronounced in some regions and some seasons than others. Despite their differing resolutions, the two datasets share many notable features on larger scales. For example, within the Great Plains region recurrence values are quite similar in both areal extent and time scale for all seasons except JJA, where in the CLM they are more extensive and shifted westward relative to the VIC-highres. Recurrence in the Great Basin is present in both datasets but generally at much longer leads in the VIC-highres than CLM. Results appear to be notably dissimilar during JJA except in the Southwest where both datasets have fairly similar values [i.e., TR is less (greater) than 10 months in the eastern (western) part of the box]. Also, in some areas (such as the southwestern and northeastern United States), significant values of TR exist all or most of the year for both datasets, but their time scales change by season in a manner consistent with reemergence as described in Fig. 2b. For example, in the Southwest region TR decreases by roughly 3-month increments (going from red to blue) in each panel from DJF through SON (Figs. 7a and 7d for CLM, and Figs. 7e and 7h for VIC-highres). On the other hand, some regions have significant values of TR only for specific seasons. For example, in the Pacific coastal states, TR seems primarily dependent upon winter soil moisture anomalies (cf. Figs. 7a and 7e, and to a lesser extent Figs. 7d and 7h), whereas TR is most related to spring soil moisture in an area of the eastern Great Plains (Figs. 7b and 7f) that shifts westward (Figs. 7c and 7g) and substantially enlarges for summer anomalies in CLM. Further sensitivity of TR to time period and dataset is shown in Fig. S4.

b. Regional soil moisture memory and reemergence

The variability statistics within the above datasets appear to agree better on larger spatial scales. This is also true for the other NLDAS2 products (Dirmeyer et al. 2016). To investigate reemergence on these larger scales, we constructed area-averaged time series for a few selected regions as described in section 3. We then determined both the root zone soil moisture and precipitation autocorrelation functions and the cross correlation between the root zone soil moisture and precipitation, all as a function of the annual cycle. Additionally, we determined the cross correlation of root zone soil moisture with the vertical profile of soil moisture for each season of the year. In the following, we show results using the CLM dataset since it has the most detailed vertical structure; similar analysis performed with the VIC-highres dataset yielded generally similar results (see section 4c).

The annual cycle of the root zone soil moisture autocorrelation function for the SW time series (Fig. 8a) shows its memory more than doubled (from ~3 to ~8 months) between spring and late fall. For autocorrelation functions starting from summer and early fall months, a secondary maximum extends diagonally from an 8-month lag for SON to a 12-month lag for MJJ. That is, significant autocorrelation values recur during the subsequent summer, which is also consistent with TR values in the southwestern United States (Figs. 7b,c). This recurrence also continues for a second year, with significant autocorrelation values at lags up to 24 months centered on late summer/early fall.

Fig. 8.
Fig. 8.

Soil moisture statistics for the SW time series in the CLM dataset, for the years 1950–2010. Annual cycle of the autocorrelation function of (a) root zone soil moisture anomalies and (b) precipitation anomalies; (c) annual cycle of precipitation–root zone soil moisture cross correlation. In (c), positive lags refer to precipitation lagging soil moisture (i.e., soil moisture leading precipitation) and negative lags refer to precipitation leading soil moisture. For example, the location (4, DJF) indicates the correlation of DJF root zone soil moisture anomaly with the precipitation anomaly the following AMJ (i.e., 4 months later), while the location (−6, MJJ) indicates the correlation of MJJ root zone soil moisture anomaly with the precipitation anomaly the previous NDJ (i.e., 6 months earlier). (d)–(g) Cross correlation between the root zone soil moisture anomaly [in (d) DJF, (e) MAM, (f) JJA, and (g) SON] and the soil moisture anomaly as a function of depth and lead/lags. For example, in the SON panel the location (5, −0.5) indicates the correlation of SON root zone soil moisture anomaly with the soil moisture anomaly at depth 0.5 m in the following year FMA season (i.e., 5 months later); the location (−5, −0.8) in the DJF panel indicates the correlation of DJF root zone soil moisture anomaly with the soil moisture anomaly at depth 0.8 m in the previous year’s JAS season (i.e., 5 months earlier).

Citation: Journal of Climate 32, 10; 10.1175/JCLI-D-18-0540.1

Soil moisture reemergence is apparent in the cross correlation of the DJF (Fig. 8d), MAM (Fig. 8e), JJA (Fig. 8f), or SON (Fig. 8g) root zone soil moisture anomaly with soil moisture anomalies at all lead/lags and depths. DJF and MAM root zone anomalies appear to descend below 1-m depth over a period of several months, reminiscent of Fig. 1. JJA (Fig. 8f) and SON (Fig. 8g) root zone soil anomalies also descend but not as deeply. DJF and MAM root zone soil moisture anomalies seem mostly correlated to future anomalies rather than to past anomalies, whereas JJA and SON root zone anomalies are significantly correlated to past anomalies as well. These panels all show an apparent reemergence signal in which the secondary autocorrelation function maximum (Fig. 8a) occurs when higher deep layer soil moisture memory reaches the surface from below.

Precipitation has less memory than root zone soil moisture (Fig. 8b), except in spring, and generally leads soil moisture (Fig. 8c), both as expected. However, November–January (NDJ) precipitation is also highly correlated with root zone soil moisture anomalies throughout the following winter and spring, even more than precipitation during the intervening months. For example, May–July (MJJ) root zone soil moisture is slightly more correlated with precipitation six months earlier (NDJ) than it is one month earlier (AMJ). This could be consistent with NDJ precipitation forcing a soil moisture anomaly that persists and/or reemerges in late spring. Also, at some times when precipitation and root zone soil moisture recurrences appear to coincide, the cross-correlation function suggests that soil moisture leads precipitation (cf. maxima in Figs. 8a–c).

In the Great Plains (Fig. 9), soil moisture reemergence appears to occur in springtime. Higher soil moisture autocorrelation values at longer lags are fixed to the early-to-middle spring season (Fig. 9a), with a secondary maximum extending diagonally from about a 6-month lag starting in JAS to about a 12-month lag starting in MAM. The vertical correlation structure again shows apparent descent of soil moisture anomalies, reaching a greater depth than for the SW possibly because GP soil conditions are comparatively more moist (Kumar et al. 2016). Springtime root zone soil moisture anomalies that recur the following year in early spring (Fig. 9a) appear driven by reemergence (Fig. 9e). Some signs of springtime reemergence also seem present for prior wintertime anomalies (Fig. 9d), but they do not quite reach the surface. There may also be a second-year reemergence centered in winter (cf. Figs. 9d and 9e to the recurrence at lags of 20–24 months in Fig. 9a). In contrast, there is significant 2-yr anticorrelation for summertime (JJA) soil moisture anomalies, also extending to deeper depth (Fig. 9f), which could be consistent with ENSO forcing (Yang et al. 2007). Note also that the weak precipitation recurrence seen between spring months and JJA (Fig. 9b) does not match the root zone soil moisture recurrence (Fig. 9a). Moreover, while winter/early spring root zone soil moisture anomalies are not strongly correlated with the previous month’s precipitation, they are correlated with precipitation from the previous fall [e.g., October–December (OND); Fig. 9c]. This relationship is consistent with the longer root zone memory seen at that time of the year (Figs. 9a and 9g) and also with recurrence from the previous spring (e.g., MAM; Fig. 9c), consistent with reemergence of the previous spring’s soil moisture anomalies in Fig. 9e.

Fig. 9.
Fig. 9.

As in Fig. 8, but for the GP time series.

Citation: Journal of Climate 32, 10; 10.1175/JCLI-D-18-0540.1

Analysis for the Great Basin (Fig. S5) yields broadly similar features, but the GB time series has much longer soil moisture memory (~12 months) from late fall through early spring months than during the summer (~4 months), even as its precipitation has generally less memory than the SW and GP regions. The reemergence signal appears in the longer memory season (e.g., DJF and SON). This longer memory might be related to snow and soil freezing processes; however, data uncertainty due to poorly resolved topography in the CLM could also be an issue (Lawrence et al. 2019, manuscript submitted to J. Adv. Model. Earth Syst.).

c. Sensitivity to dataset

1) Other LDAS datasets

Sensitivity of these results to the LSM used was assessed by repeating the above analyses across the different LDAS products (CLM, VIC-highres, Noah, Mosaic, GLEAM, SMERGE, and MERRA-2) over the common 1980–2010 period. The resulting TR maps (Fig. S4) show recurrence patterns that while broadly consistent have some fairly obvious quantitative differences.

The root zone soil moisture autocorrelation functions of the SW time series for all LDAS datasets and their ensemble mean, for the years 1980–2010, are compared in Fig. 10. Also shown is the VIC-highres results for 1950–2010, which compares very well with the CLM for that period (Fig. 8a). The overall details, in particular recurrence magnitudes and time scales, are quite consistent between the two time periods in the VIC-highres, and across all LDAS datasets and the ensemble mean for 1980–2010. Soil moisture anomalies appear to reemerge during late summer from prior anomalies more than a year in advance. For example, DJF (AMJ) anomalies have a secondary maximum 20 (16) months later, during August–October (ASO). As in Fig. 8, reemergence appears to occur in two successive summer seasons: SON soil moisture anomalies reemerge 8 months later, and again 22–24 months later.

Fig. 10.
Fig. 10.

Annual cycle of root zone soil moisture anomaly autocorrelation function for the SW time series, in LDAS datasets. All figures represent results from 1980 to 2010, except for the top row center, which shows 1950–2010. Results for the ensemble mean for 1980–2010 are shown in the second row left corner.

Citation: Journal of Climate 32, 10; 10.1175/JCLI-D-18-0540.1

The results for the GP time series (Fig. 11) are qualitatively similar across the datasets but have less quantitative agreement than in Fig. 10. Greater differences also exist between the post-1980 period and the full period in both the VIC-highres and CLM (Fig. 9a) and VIC-highres. The ensemble mean shows a stronger reemergence signal than the individual LDAS datasets, although all show significant recurrence during Fall; for example, February–April (FMA) soil moisture anomalies recur 8 months later (in OND), whereas AMJ soil moisture anomalies recur about 5–6 months later. Analysis of the GB time series (Fig. S6) shows even more discrepancies across the datasets, although most of the LDAS datasets have generally longer root zone soil moisture memory starting from the late fall through early spring months.

Fig. 11.
Fig. 11.

As in Fig. 10, but showing the annual cycle of root zone soil moisture anomaly autocorrelation function for the GP time series, in the LDAS datasets. All figures represent results from 1980 to 2010, except for the top row center, which shows 1950–2010. Results for the ensemble mean for 1980–2010 are shown in the second row left corner.

Citation: Journal of Climate 32, 10; 10.1175/JCLI-D-18-0540.1

2) Comparison to in situ data

Finally, we compare to the limited in situ records. Figure 12 shows the Illinois root zone soil moisture autocorrelation function for the ICN and LDAS datasets. All show reemergence signals in their autocorrelation functions, but they appear to agree less well than in Fig. 11, perhaps because of the smaller area or shorter data period. In fact, Noah shows significant negative autocorrelations, although SMERGE, which uses the Noah model to assimilate remote sensing–based surface soil moisture observations, does not. Still, most of the LDAS datasets agree better with each other than they do with the ICN. These differences are obviously concerning and could stem from deficiencies of the LDAS datasets (e.g., Dirmeyer et al. 2016), at least in the Illinois region (Xia et al. 2014). However, issues such as the scale mismatch between climate model grids and local ICN observations, the limited spatial and temporal sampling of the ICN dataset itself, and spatial heterogeneity in soil characteristics could also be impacting our correlation analysis. To test this possibility, we resampled the VIC-highres dataset using the days and 1/16° grid boxes that best corresponded to the available ICN data (no more than 18 locations and one to a few instantaneous samples per month), and then took the average over all the subsampled data to create the “VIC-highres-subsample” Illinois monthly time series. This produced a much better match to the ICN than did the original monthly mean data: the ICN and VIC-highres-subsample time series are notably better correlated, especially in the cold season (see appendix A), and extrema within the autocorrelation functions based on the VIC subsampled data and ICN (Fig. 12) also have considerably better correspondence. Additionally, the autocorrelation function and associated reemergence show substantial variation across all the individual ICN stations (Fig. S7), more often showing a stronger reemergence signal in the southern Illinois sites. Similar issues impact evaluation of soil moisture reemergence in the vertical cross sections (see Figs. S8 and S9). Given all of these considerations, it appears to be difficult to draw firm conclusions from the ICN results, at least quantitatively.

Fig. 12.
Fig. 12.

Annual cycle of root zone soil moisture autocorrelation function for Illinois from all soil moisture dataset (cf. Table 1). Ensemble mean results include all soil datasets shown here except for the subsampled version of the VIC-highres.

Citation: Journal of Climate 32, 10; 10.1175/JCLI-D-18-0540.1

Figure 13 shows the root zone soil moisture autocorrelation functions at six other sites with relatively long records and with soil moisture measurements down to a depth of at least 40 cm. These show that autocorrelation structures with significant differences from simple exponential decay are prevalent across observation sites throughout the United States. For example, three (Mandan, Long Valley, and Reynold’s Creek) out of six sites show robust reemergence signals. The remaining three sites also show reemergence signals, but they are weak and not statistically significant; two sites have some negative correlations originating in winter that might be due to precipitation forcing and/or data uncertainty due to snow cover (Quiring et al. 2016). A comparison of 13 years of LDAS data at Reynold’s Creek site shows qualitatively similar results (e.g., the reemergence signal in the summer and fall seasons; Fig. S10). Results for the different sites seem to somewhat correspond to the LDAS results discussed above, but again the limited sample sizes and localized nature of the in situ measurements make a more detailed assessment difficult.

Fig. 13.
Fig. 13.

Annual cycle of root zone soil moisture autocorrelation for selected in situ sites (see text for more details, and Fig. A2 for site locations).

Citation: Journal of Climate 32, 10; 10.1175/JCLI-D-18-0540.1

d. Sensitivity to precipitation variability

One obvious issue raised by the precipitation correlations in section 4b is whether root zone soil moisture recurrence truly represents reemergence and other land surface processes, or whether it is largely driven by recurring atmospheric forcing (e.g., precipitation; Figs. 8b and 9b). Similarly, significant negative soil moisture autocorrelation could represent atmospheric rather than land effects, either due to oceanic forcing or to sampling of random weather events. On the other hand, while the observed precipitation recurrence could be due to climate forcing, Figs. 8c and 9c suggest it could also result from land feedbacks—for example, from atmospheric coupling to a root zone layer responding to soil moisture reemergence. To initially explore these issues, we compared the VIC-lowres soil moisture dataset to two corresponding VIC-lowres datasets used in Livneh and Hoerling (2016), which were created using observed atmospheric forcing as before except 1) the precipitation variability was removed (i.e., precipitation was fixed to its annual cycle; “precip climo”), or 2) the temperature variability was removed (i.e., temperature was fixed to its annual cycle; “temp climo”). We also compared to the CPC soil moisture dataset that, while also forced with observations, had no vertical structure in its LSM. Since the CPC dataset represents a 1.6-m-thick surface layer, we compared to the top 1 m (rather than top 0.4 m) soil moisture from the VIC-lowres datasets; this mainly tended to slightly lengthen overall memory and thereby weaken reemergence strength relative to results using the top 0.4-m layer but had no other qualitative impact.

Figure 14 shows the SW autocorrelation function in the four different datasets. Removing observed precipitation variability yielded a reduction of the correlation between fall and subsequent spring soil moisture, which could be due to removing persistent cool season ENSO forcing in the Southwest (note in Fig. 8b that the fall/winter precipitation autocorrelation is significant for lags of up to 5 months). Still, some soil moisture recurrence remains, suggesting that it may not only be forced by precipitation. Additionally, for lags greater than about 6 months, recurrence was not reduced; instead, it appears that the precipitation variability may even have obscured a stronger summertime reemergence signal. Removing temperature variability, in comparison, had minimal effect. It is interesting to note that even the very simple CPC hydrology model showed a similar recurrence pattern in the second year. This supports climate forcing (precipitation and evaporative demand) as a key driver compared with soil moisture vertical discretization in the model, although it does not rule out possible land–atmosphere feedbacks related to reemergence.

Fig. 14.
Fig. 14.

Annual cycle of top 1-m soil moisture autocorrelation for the SW time series, from different VIC-lowres datasets based on (a) observed forcing (cf. Fig. 11), (b) observed temperature and climatological precipitation forcing (“precip climo”), and (c) climatological temperature and observed precipitation forcing (“temp climo”), for the years 1950–2010. (d) The corresponding analysis applied to the same region and period in the CPC (“leaky bucket”) dataset. Note that unlike previous figures, these results are for the 0–1-m soil layer, except for CPC, which represents 0–1.6 m.

Citation: Journal of Climate 32, 10; 10.1175/JCLI-D-18-0540.1

Figure 15 shows the same analysis for the GP time series. Here we see no reduction in autocorrelation values when precipitation variability is removed; in fact, since anomaly recurrence at longer lags is amplified, it again appears that precipitation variability may have partly obscured a stronger reemergence signal that also clearly extended to a second successive spring. Moreover, the recurrence signal is notably weaker in the CPC dataset, especially in the second year, further supporting the importance of GP reemergence. For the GB time series, in contrast, precipitation variability appears to drive the bulk of the persistence and reemergence signals except for a weaker signal during the warm season (see Fig. S11). However, given the poorer agreement across the LDAS datasets for the arid GB region, confidence in this result is low.

Fig. 15.
Fig. 15.

As in Fig. 14, but showing the annual cycle of top 1-m soil moisture autocorrelation for the GP time series, from different VIC-lowres datasets based on (a) observed forcing (cf. Fig. 12), (b) observed temperature and climatological precipitation forcing (“precip climo”), and (c) climatological temperature and observed precipitation forcing (“temp climo”), for the years 1950–2010. (d) The corresponding analysis applied to the same region and period in the CPC (“leaky bucket”) dataset.

Citation: Journal of Climate 32, 10; 10.1175/JCLI-D-18-0540.1

5. Concluding remarks

In this study, we aimed to investigate mechanisms of long-term soil moisture memory, using a statistical (i.e., correlations-based) analysis of in situ observations and LDAS datasets over North America. We defined and identified for the first time a “soil moisture reemergence” process, which could lead to improved understanding of long-term drought and pluvial processes and also be a source of soil moisture predictability on seasonal to interannual (or possibly longer) time scales.

In the extratropical oceans, the memory time scale of upper ocean thermal anomalies is on the order of a few seasons. Yet, both observational and modeling studies have shown that extratropical sea surface temperature anomalies tend to recur from one winter to the next, even as they do not typically persist during the intervening summer, due to a process Alexander and Deser (1995) called reemergence (Alexander and Deser 1995; Alexander et al. 1999; Namias and Born 1970). In the ocean, reemergence occurs because wintertime thermal anomalies are well mixed downward throughout the deep winter mixed layer, become decoupled from the surface when the mixed layer shallows in the summer, and are re-entrained into the mixed layer as it deepens the following winter. Soil moisture reemergence is an analogous process because it too represents strong seasonal modulation in the coupling between a surface layer with short memory and a deeper layer with longer memory, wherein 1) in the first season, surface forcing creates an anomaly that propagates into the deep layer; 2) in the next season, the layers are effectively decoupled so that the anomaly decays at the surface but persists in the deep layer; and 3) eventually, coupling is reestablished, driving the surface back toward its prior anomaly. In the ocean, this process has a clear signature in the seasonally varying autocorrelation function: a secondary maximum tilted diagonally so that it is tied to a fixed season rather than a fixed lag (Newman et al. 2003). That a similar feature also appears in the root zone soil moisture autocorrelation function (e.g., Figs. 2a, 8a, and 9a) is evidence for a similar reemergence process for soil moisture.

Nevertheless, it is important to clearly distinguish between our results and our interpretation of them, since ultimately we believe this study raises more questions than it answers. Primarily using long-term (60 yr) LSM-based (LDAS) soil moisture datasets, we have found statistically significant recurrence of root zone soil moisture seasonal anomalies for lags as long as 2 years, which is considerably longer than the generally accepted memory time scale of root zone anomalies. This recurrence is usually strongly related to the seasonal cycle, so it is often apparent only during isolated seasons and not year-round. These results immediately suggest that root zone soil moisture is likely predictable on time scales measured in seasons and maybe even years, not just months.

We interpret these results as evidence of a soil moisture reemergence process, not only due to the diagonal features in the autocorrelation function, but also because at the same time there appears to be propagation of anomalies to the deeper soil in some seasons with the later reemergence of these anomalies. This is our interpretation of the vertical cross-section plots (Figs. 8d–g and 9d–g) where the recurrence of root zone soil moisture anomalies (corresponding to Figs. 8a and 9a) was better correlated with prior deep layer anomalies than to either the root zone anomalies of the previous season or to atmospheric forcing (i.e., precipitation). Experiments with the lower-resolution version of the VIC model also suggest that atmospheric variations alone cannot explain the observed recurrence.

We hypothesized two possible mechanisms: 1) the demand-driven hypothesis and 2) the anomaly propagation hypothesis. Data presented here are consistent with both hypotheses. Additional observations and numerical experiments are needed to quantify their relative contributions. For example, data from the multidecadal drought period may clarify the role of the anomaly propagation hypothesis. Similarly, numerical experiments with and without deep layer soil moisture memory and its impacts on soil moisture anomalies during the summer may clarify the role of the demand-driven hypothesis.

One of the underappreciated implications of oceanic reemergence is that extratropical decadal variability and predictability may have pronounced seasonality. That is, a decadal signal may only exist in one particular season, not necessarily year-round. This may also be true for predictability stemming from soil moisture reemergence. Also, note that much of the PDO’s variability results from reemergence acting to redden the ENSO signal in the North Pacific (Newman et al. 2016). It is an interesting question whether soil moisture reemergence might act similarly to redden the ENSO signal over land, and if so whether this is why, as previously suggested by Newman et al. (2003), there is an apparent pronounced PDO signal in North American drought (Barlow et al. 2001) and in climate proxies such as tree rings (Biondi et al. 2001; D’Arrigo and Wilson 2006).

In summary, while much of the evidence put forth here in support of soil moisture reemergence is compelling, it is also largely circumstantial due primarily to the lack of direct observations needed, ICN data notwithstanding—hence the caveat “potential reemergence” in the paper title. Our statistical analysis suggests a new and interesting physical process, but multiple questions remain: the extent to which the process exists, how consistent it is with our physical hypotheses, and how quantitatively important it is to the land–atmosphere climate system. Since our analysis was limited to relatively shorter in situ and only somewhat longer model-based datasets, its considerable quantitative uncertainty could reflect sampling issues, meaning that longer data records (which may be unavailable) are required to isolate reemergence from weather and climate variability and land–atmosphere coupling. However, we also cannot exclude the possibility that reemergence acts quite differently in the current generation of LSMs than it does in nature. Many potentially interacting but largely undetermined factors can also affect soil moisture reemergence, including precipitation variability and persistence, land–atmosphere coupling, and the distribution of soil types both horizontally and vertically. LSM representation of reemergence could be additionally complicated by factors including (but not limited to) vertical discretization and soil moisture model parameterizations, and by how well they represent seasonal and regional variations of all the above variables. For example, Livneh et al. (2015a) found that the same LSM produced different portrayals of long memory processes like drought when driven with different underlying soil survey data. In particular a rigorous sensitivity analysis of the role of model parameter settings and layer discretization would be needed to assert a more quantitative measure of reemergence beyond the qualitative assessment presented here. The effects of land use land cover type, interactive vegetation phenology, and hydraulic redistribution by the plant root system could also be relevant. Finally, while we ruled out significant impacts on our results by a seasonally varying linear trend, more complex effects of anthropogenic change are still possible. Addressing all of these questions will require additional analysis of related hydrological observations and a systematic experimental framework ranging from simple multivariate autoregressive models to stand-alone land models and complex coupled climate models.

Acknowledgments

The authors thank three anonymous reviewers for comments that greatly improved this paper. This work was supported by NOAA/CPO. Sanjiv Kumar’s contribution was supported by NRC Research Associateship Award at NOAA/ESRL/Physical Science Division, and USDA Hatch Grant ALA031-1-18023.

APPENDIX A

Station Data Processing

a. Processing of ICN data

At each of 18 sites throughout Illinois (see Fig. A1), ICN observations were taken at least twice per month during the growing season, which we averaged together, and once per month otherwise for the years 1983–2004 (although irregular sampling meant that some months were skipped at some stations in some years). These measurements were then taken to represent the monthly averages at each site. Each soil layer was processed separately; if a layer was missing it was filled in with weighted linear interpolation, but if more than one layer was missing from the root zone and two layers were missing from the deep layer the site was recorded as missing for that month. Then, we determined the root zone (0–0.4 m) soil moisture at each site for each month, and subsequently averaged the monthly root zone soil moisture across the available sites each month to represent the Illinois average root zone soil moisture total field. ICN soil moisture data were available from 1983 to 2004 for most of the stations, but the first two years were excluded due to outliers that were more than four standard deviations away from the mean of all data (Xia et al. 2014).

Fig. A1.
Fig. A1.

Locations of station data and the boundaries for the three regional indexes used in this study.

Citation: Journal of Climate 32, 10; 10.1175/JCLI-D-18-0540.1

Figure A2 shows the Illinois-mean seasonal anomaly correlations of ICN soil moisture data with the LDAS datasets for the root zone (0–0.4 m). All LDAS anomalies are generally better correlated with ICN anomalies during the growing season (spring and summer) than the winter seasons, as was earlier found by Xia et al. (2014). For example, VIC-highres shows an anomaly correlation of ~0.9 from AMJ through ASO seasons but drops below 0.5 for DJF through FMA seasons. VIC-highres anomalies generally correspond better with the ICN compared to other LDAS datasets for most of the year.

Fig. A2.
Fig. A2.

Correlation of ICN mean root zone soil moisture anomaly with corresponding anomaly from each soil moisture dataset averaged within Illinois, as a function of season for the years 1985–2004. Note that the CPC dataset represents soil moisture in the 0–1.6-m layer. Ensemble mean results here include all datasets except CPC, and the subsampled version of the VIC-highres. Three instances of VIC are included to illustrate differences in model scale configuration, as well as the importance of subsampling daily model outputs on the sampling dates and location of the ICN stations.

Citation: Journal of Climate 32, 10; 10.1175/JCLI-D-18-0540.1

To investigate the issue of sparse and irregular temporal frequency of ICN observations, we subsampled VIC-highres soil moisture data to the nearest location (1/16° grid box) and day of observation at the respective stations before taking the area and monthly average; the number of stations each month varied consistent with ICN data availability. This time series, called the VIC-highres-subsample, has notably higher correlations with the ICN monthly time series, especially throughout most of the cold season (Fig. A2). This suggests that the effect of sampling (primarily temporal; not shown) at the ICN sites is nontrivial, and likewise that LDAS datasets (at least the VIC-highres, at these locations, for 3-month averages) may better represent in situ data than the comparison in Xia et al. (2014) suggests. Spatial heterogeneity in soil characteristics may likewise be an issue. If all this is the case, it may even be that the full monthly averaged Illinois-mean VIC-highres time series is as good or even better a representation of soil moisture over the 1982–2015 period than the ICN time series.

b. Processing of other station data

We also examined raw station data from sites other than the ICN. Data were downloaded from the ISMN website (http://ismn.geo.tuwien.ac.at), selected in or near the predefined regions (GP, SW, and GB). We found six stations (2 from SCAN, 3 from SNOTEL, and 1 from ARM) that all have a record length of at least 12 years and soil moisture observations down to at least 0.5 m. Some other stations or networks that also have relatively long records contained too much missing data (e.g., the SNOTEL station SILVIES) or were systematically missing certain months of the year (e.g., the IOWA network) to make for a representative determination of the seasonal cycle of the autocorrelation function.

APPENDIX B

Autocorrelation Function and Significance Testing

The autocorrelation function was determined separately for each month by correlating the soil moisture anomalies at time = 0 with values at lags and leads ranging from −24 months to +24 months. This was done both for the same soil layer [autocorrelation (AC)] and between two different soil layers [cross correlation (CC)]. Let us suppose that is the seasonal anomalies time series where subscript y represents year (1–n), m represents season (1–12), and l represents soil layer; then the correlation functions are given as below:
eb1
eb2
where is autocorrelations for season m, layer l, and at lead/lag , which ranges from −24 to 24. The term is the cross correlation between layer for season m and lead/lag ; Correl is the linear correlation coefficient between the two series. For , = , and , = . We determined the t statistic for the regression coefficient and converted the t statistic into the statistical probabilities (p value). Thus, every year contributes one sample in the given time series, (e.g., ). We determined degrees of freedom by accounting for serial autocorrelation in the time series and accordingly reducing the effective sample size using the NCL function equiv_sample_size (NCL 2018). For example, the number of degrees of freedom for 20 years of Illinois seasonal anomalies was 16. We label AC or CC values with a p value ≤ 0.05 for two-tailed test as statistically significant.

Additionally, for every significant AC and CC value we tested whether it represented a linear relationship, by finding the linear, quadratic, and cubic least squares fits to the data used to determine the correlation value (examples are shown in Fig. S12). The Bayesian information criterion (BIC) test was then applied in each case to select which of these three curves was the best model of the data scatterplot. We found that in 94% of the values tested, the linear fit was the best.

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