Supplemental Information for: Patterns of plant rehydration and growth following pulses of soil moisture availability

Reviewer 1: This study assesses the temporal pattern of soil moisture and plant water content derived from SMAP to understand plant responses to precipitation pulses, which have shown signiﬁcant lags in ﬁeld studies. The comprehensive spatial scale of this analysis is impressive and timely. Importantly, the authors use a daily LAI product for Africa to account for the combined growth and rehydration signal inherent in VOD interpretation. I have some concerns about the correct use of Kruskal-Wallis tests and found the comparison between spatially average temporal VOD trends and results of a 1D SPAC model somewhat spurious. Authors: Thank you for your constructive comments on our study. We will address your

. Percentage of pulses with 1≤tp≤3 where VOD increases before the drydown initiation (during the storm). Only regions with median tp ≥1 are shown. The inset shows the spatial distribution of the metric.

S2. tp Estimation Uncertainty
Fig. S3. tp biases due to effects of SMAP's 2-3 day rather than daily sampling frequency. Simulation with expected behavior of VOD during drying as found in (Feldman et al., 2018). True tp magnitudes vary randomly. Fig. S4. Effects of sampling on tp estimates binned as a function of true tp. The Nyquist frequency for SMAP is approximately 0.2 per day (5-day period). This results in larger variance of tp estimates when true tp is less than the Nyquist period.

S3.1 Plant Components
To investigate the underlying mechanisms that alter plant rehydration timescales, we evaluate plant hydraulic storage timescales under varying conditions after a surface soil moisture pulse using a plant hydraulic model. We specifically choose a one-dimensional SPAC model, assessed in previous studies (Carlson and Lynn, 1991;Hartzell et al., 2017;Lhomme et al., 2001;Zhuang et al., 2014). This model uses governing equations based on the cohesion-tension theory of water potential-driven vertical flow from soil to atmosphere, but has fewer discretized soil and plant components than more complex SPAC model formulations (Mackay et al., 2015; 79% al., 2016, 1998). This relative simplicity is advantageous because of its reduced number of parameters. The SPAC model formulation explicitly represents root-zone soil, root, xylem, and leaf components, and accounts for plant storage. It is a balance between incoming sap flow and transpiration losses in the xylem in terms of water potential: C

Sampling Frequency + Algorithm + Noise
where y is water potential, R is resistance, and C is capacitance. x, w, s, r, and L subscripts represent xylem, plant-storage, root zone soil, root (soil interface and radial), and leaf components, respectively. The components are shown in Fig. S7. Rx and Rr are set equal due to lack of field parameterizations and each are referred to as plant resistance (RP) in our simulations. This simplification precludes finer analysis of individual effects of xylem embolism and root-soil interface resistances, but provides a framework to analyze of how whole-plant resistances influence hydraulic timescales. Rw is allowed to decrease with reductions in yw (Carlson and Lynn, 1991): Rw0 is the storage resistance at full capacity when RWC is 1 and is set equal to Rx (or RP) here due to lack of field information. Relative water content (RWC) is estimated as linearly related to yw: This requires an assumption of a lower limit (yCrit) placed on yw. yCrit is chosen to be -10 MPa with alterations to this value having little impact on results. Transpiration is computed based on a mass transfer model: Vapor pressure deficit (VPD) reaches zero by predawn and a maximum at midday which is a variable drawn within the SPAC simulations. e is the ratio of dry air and vapor gas constants, or 0.622. The surface pressure (p), water density (rw), and air density (rair) are taken to be 100 kPa, 1,000 kg/m 3 , and 1.2 kg/m 3 . Rs is computed based on the Medlyn stomatal conductance model and is scaled to a canopy scale parameter by normalizing by LAI (Medlyn et al., 2011): where g0 and g1 are model parameters assuming savanna values to be -0.007 mol m -2 s -1 and 6 kPa 1/2 , respectively. Ambient CO2 concentration (Ca) is assumed constant at 400 µmol/mol. Net assimilation rate (A) is decreased from 6 to 4 µmol m -2 s -1 over the duration of drying (Xu and Li, 2006). The aerodynamic resistance of turbulent, vertical transport of vapor is computed based on neutral conditions (no surface-air temperature gradient): The wind speed (v) is held constant for a height of 2 m (z) and is variable based on drawn values within the simulations. The vegetation height is taken to be 0.5 m (for shrubs and grasses) and as such the estimated roughness height (z0) is 0.05 m and estimated zero plane displacement (d) is 0.375 m. The von Karman constant, k, is 0.41.

S3.2 Soil Component -Infiltration
Moisture pulse infiltration to the root zone is additionally assessed. We compute yS at each 5 cm layer from 0 to 1 m by numerically solving the soil water balance with Richard's equation to determine the time of unsaturated flow from the rain-wetted surface soil layer to the root zone: where q is soil moisture and K is unsaturated hydraulic conductivity. Note that Eq. S8 takes the same form as Eq. S1 (with Ohm's law analogy) with a potential gradient from surface to root zone, the inverse of K serving as soil resistance, and integral of soil layer depth representing soil storage capacitance. Soil retention curves are used to define the relationship between root zone soil moisture (q) and potential (ys) as well as soil hydraulic conductivity (K) (Brooks and Corey, 1966): S10) b is the Brooks-Corey parameter which also defines c, or 2b+3. n is porosity. Soil moisture decay is imposed as a boundary condition in the top layer. In semi-arid regions globally, the e-folding decay rate for surface soil moisture is approximately 10 days (McColl et al., 2017). Losses due to plant water uptake, soil evaporation, and percolation are encompassed in this loss rate. Soil moisture is assumed to decay uniformly during the time period instead of slowed decay overnight as in (Daly et al., 2004). After the soil pulse reaches the lower layers, each above layer decays with the boundary condition. All layers below 0.05 m are assumed to decay four times slower than the surface layer due to reduced impacts of soil evaporation (Gebauer et al., 2002). Z defines the layer where ys is coupled to the SPAC model.
Note that the SPAC model does not account for many factors including the effects of osmotic adjustment under drying. However, more complex parametrizations include uncertainties with more parameters, especially those not that well constrained by previous measurements. This exemplifies the importance to bear in mind the multi-dimensional parameter space underlying this model and thus the wide range of scenarios that may influence time variations of plant and soil potentials.

S3.3 SPAC Model Simulation General Notes
Using the SPAC model, yW time series are simulated following soil moisture pulses in order to investigate how different factors influence the simulated pulse response timescales. A three-day spin-up period allows the plant and soil water potential components to come to an initial equilibrium. An additional two-day drying period is implemented before the surface moisture pulse. The model is run at a 3 second time step. This 3 second time step and 0.05 m soil layer intervals prohibits model "break down" when solving explicitly. A rain pulse occurs at 6:00 AM after the two-day drying period. The pulse is followed by eight days of drying. tp is computed as the peak yW following the pulse, analogously to the satellite-observed plant water content. This simulation is repeated using a Monte Carlo approach (n = 1,000), randomly sampling SPAC model parameters from given parameter ranges based on previous field measurements. tp sensitivity to a given parameter is evaluated by fixing the respective parameter and randomly varying all other parameters ("All" scenario). To evaluate pairwise interactions between sets of two parameters, an additional parameter to that in the "All" scenario is fixed and all other parameters are randomly varied.
The SPAC model parameter space is bounded to common semi-arid meteorological conditions and plant types (Table S1; see also SI for parameter bound justification based on available databases (Kattge et al., 2020) and measurements from the literature). Dryland plants and climatic conditions are chosen for investigation as global drylands primarily are found in this study to exhibit multi-day rehydration (slow rehydration). The SPAC model is used to evaluate the scenarios under which plant-storage water potential timescales exceed a day. The stomatal and plant resistances are linearly decreased over three days to randomly varying degrees (RP recovery and RS impairment factors in Table S1) following the soil moisture pulse, common occurrences following rewetting due to drought recovery mechanisms (Martorell et al., 2014;Rodriguez-Dominguez and Brodribb, 2020;West et al., 2007).

S3.4 SPAC Model Parameter Range Justification S3.4.1 Whole Plant Resistance (Rp) and Its Recovery
We consult the TRY plant trait database and a review article for whole plant conductance values (Kattge et al., 2020;Mencuccini, 2003). Across species the whole plant conductance distribution is approximately lognormally distributed. We convert to plant resistance (normalized on a per leaf basis) with approximate 5 th , 50 th , and 95 th percentiles of 5x10 6 MPa s/m, 3x10 7 MPa s/m, 1x10 8 MPa s/m respectively. While this is across species, dryland grass species are comparable to this distribution at approximately 2x10 7 MPa s/m (Carlson and Lynn, 1991;Hunt and Nobel, 1987). Further, Rp can increase by up to a factor of ten from nominal to dry conditions (Brodribb and Cochard, 2009;Rodriguez-Dominguez and Brodribb, 2020;Trifilò et al., 2004;Zarebanadkouki and Carminati, 2014). Therefore, we set the Rp range between 1x10 6 MPa s/m and 1x10 9 MPa s/m.
If the plant is dried for a period, Rp increases. Upon rewetting, Rp can take two to four days to recover and decrease by a factor of five along an approximately linear trend in time (Lo Gullo et al., 1998;North and Nobel, 1995). We therefore allow Rp to decrease by a factor of one to ten linearly for approximately three days. Given the lower confidence of this Rp factor of recovery measure, we allow it to decrease by up to a factor of ten.

S3.4.2 Rooting Profile Depth
We consult the TRY plant trait database and find roots to typically located within the first meter of soil (Kattge et al., 2020). In general, semi-arid grasses tend to have most roots located between 0.1 m and 0.6 m below the surface while shrub rooting profiles are between 0.3 m and 0.7 m below the surface . We therefore allow rooting profiles to vary between 0.1 and 1 meters.

S3.4.3 Capacitance
Semi-arid grass and shrub species have capacitance values that range between 1x10 -6 m/MPa and 1x10 -4 m/MPa (Carlson and Lynn, 1991;Hunt and Nobel, 1987;Hunt Jr et al., 1991;Nobel and Jordan, 1983). Succulent and tree species tend to have values above 1x10 -3 m/MPa (Carlson and Lynn, 1991;Meinzer et al., 2003;Scholz et al., 2007), and we do not anticipate these plant functional types will dominate the satellite view. Therefore, we constrain capacitance values between 1x10 -6 m/MPa and 1x10 -4 m/MPa. Values are normalized on a unit area basis. Please note that these ranges are formulated from a scarce number of available measurements (Scholz et al., 2011).

S3.4.4 Stomatal Resistance Impairment Factor
We allow for stomatal resistance to decrease by up to a factor of 10. Previous measurements show stomatal conductance increases on this order over a few days following rewetting (Blackman et al., 2009;Brodribb and Cochard, 2009;Chen et al., 2010;Fereres et al., 1979;Martorell et al., 2014).

S3.4.5 Soil Water Potential Values
Soil water potential values can range greatly in arid to semi-arid regions. Dry soil conditions can create surface and rootzone water potential values commonly down to -5 MPa (Golluscio et al., 1998;Montaña et al., 1995). While the rootzone can become much drier, we choose -5 MPa as our lower bound on initial soil water potential as this provides a range of soil water potentials that can delay the infiltration front on the order of minutes to days. -0.5 MPa is selected as the upper bound of initial soil water potential as a dry soil value that may not create infiltration delays, but may create higher root resistances. Furthermore, we allow the moisture pulse to increase soil water potential at least up to -0.3 MPa as it is above the wettest initial soil water potential value, but still considered a small pulse that may not reach lower soil layers of the rootzone. The upper bound of the soil water potentials is allowed to approach zero or -0.001 for the greatest rewetting events.

S3.4.6 VPD and Wind Speed
We consult a range of values exhibited for drylands under nominal conditions from reanalysis data (GMAO, 2015). Typical values of VPD after rewetting range from 1 to 5 kPa while wind speeds reach typically up to 8 m/s (Feldman et al., 2019). Table S1. SPAC model simulation parameters. Each parameter is drawn from a uniform distribution with chosen "Lower" and "Upper" bounds shown. "Low" and "High" scenario columns represent the value a parameter is held fixed at for repeated simulations under the respective scenario. See the SI for references for parameter bounds.

SPAC Model Simulation Parameters
Lower Bound

S3.5 SPAC Model Simulation Results
High initial plant resistance that decreases over multiple days are the sufficient conditions for multi-day yw increases to occur upon soil rewetting (Figs. S8 to S11). This means that multiday plant rehydration does not occur unless plant resistance is initially high (Fig. S8A; RP≥10 7 MPa/(m/s)). Similarly, multi-day plant rehydration does not occur unless plant resistance decreases ( Fig. S8B; RP recovery factor >1). Increasing capacitance up to values common for shrub species increases the likelihood for multi-day yw increases, but cannot solely cause slow rehydration within this range of parameters (Fig. S8 "High C" cases and Fig. S9A). Even though rehydration is faster if stomatal conductance increases in time, an expected scenario in these cases (Rodriguez-Dominguez and Brodribb, 2020), multi-day rehydration can still occur (Fig. S8 "large RS impairment" cases and Fig. S9B). Environmental factors such as wind speed and VPD which influence transpiration as well as rooting depth do not influence multi-day rehydration occurrences, at least in these scenarios (Figs. S8 and S9). It is important to note that these aforementioned conditions that lead to multi-day plant rehydration do not consider soil resistance limitations (slow infiltration is dealt with separately). In these scenarios, the soil is initially only moderately dry and the pulse reaches the rootzone in the same day as the pulse. However, dry soils accompany high root resistances, for instance, and drier soils precede 1-3-day VOD increases observed in this study ( Fig. 3B and 4).
We further investigate effects of soil conductance on plant rehydration timescales by additionally varying pulse magnitude and initial soil moisture within our SPAC model simulations. Slow plant rehydration occurs if at least two of the three conditions occur: dry initial rootzone soil moisture, small rewetting pulses, and deeper roots (Figs. S10 and S11). Each one of these conditions alone is insufficient to slow plant rehydration (for example, deeper roots alone do not cause slow plant rehydration as seen in Figs. S10 and S11C). These conditions all promote a slow infiltration front due to initially high soil resistance that decreases over timeanalogously to initially high and decreasing Rp in the plant limitation cases (Fig. S10). These scenarios isolate slow plant rehydration due only to soil resistance by preventing additional limitations due to plant resistances. This is at least possible in this SPAC model where plant and soil resistances can be uncoupled. Multi-day plant rehydration occurs more frequently with an initially drier rootzone, smaller pulses, and deeper rooting profiles (Figs. S10 and S11). However, under interacting conditions, the moisture pulse will not reach the rootzone altogether, given the assumptions of homogenous soil and concentrated rootzone. Reductions in cases of multi-day plant rehydration occur for this reason at extremes of drier initial soils, smaller pulses, and deeper roots (as seen in Figs. S10 and S11). Nevertheless, for shallow rooting profiles, the infiltration front will still reach the rootzone, albeit slowly, under very dry initial soil conditions and small pulses (Fig. S10B).  Table S1 for 1,000 iterations in the "All" scenario. All other lines are generated the same as "All," but fix one additional parameter (noted in the legend) to evaluate pairwise interactions. Grey shading provides the 5 th and 95 th percentile of the multi-day rehydration occurrence variability in "All" scenarios using bootstrapping. The "low" and "high" values used to fix parameters are shown in Table S1. High and low wind scenarios are similar to "All" scenario and are not shown.  conditions. Also, RP = 10 7 MPa/(m/s) and does not decrease which isolates only soil conditions that would cause multi-day yW rehydration. yW peak timing for rooting depth of (B) 0.3 m and (C) 0.7 m (C = 10 -6 m/MPa, Wind = 5 m/s, VPD = 3 kPa, no change in RP or RS). Grey shading in (C) indicates that the pulse did not impact yW because the pulse did not reach the rootzone. High and low wind scenarios are similar to "All" scenario and are not shown.