# Confronting the water potential information gap

Kimberly A. Novick, Darren L. Ficklin, Dennis Baldocchi, Kenneth J. Davis, Teamrat A. Ghezzehei, Alexandra G. Konings, Natasha Macbean, Nina Raoult, Russell L. Scott, Yuning Shi, et al.

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Kimberly A. Novick, Darren L. Ficklin, Dennis Baldocchi, Kenneth J. Davis, Teamrat A. Ghezzehei, et al. Confronting the water potential information gap. Nature Geoscience, 2022, 15, pp.158-164. 10.1038/s41561-022-00909-2. insu-03721933

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# Confronting the water potential information gap

Kimberly A. Novick ID<fnref n="1" />✉, Darren L. Ficklin², Dennis Baldocchi ID³, Kenneth J. Davis<fnref n="4" />,
Teamrat A. Ghezzehei ID⁵, Alexandra G. Konings ID⁶, Natasha MacBean ID², Nina Raoult⁷,
Russell L. Scott⁸, Yuning Shi⁹, Benjamin N. Sulman ID<fnref n="10" /> and Jeffrey D. Wood ID¹¹

Water potential directly controls the function of leaves, roots and microbes, and gradients in water potential drive water flows throughout the soil-plant-atmosphere continuum. Notwithstanding its clear relevance for many ecosystem processes, soil water potential is rarely measured in situ, and plant water potential observations are generally discrete, sparse, and not yet aggregated into accessible databases. These gaps limit our conceptual understanding of biophysical responses to moisture stress and inject large uncertainty into hydrologic and land-surface models. Here, we outline the conceptual and predictive gains that could be made with more continuous and discoverable observations of water potential in soils and plants. We discuss improvements to sensor technologies that facilitate in situ characterization of water potential, as well as strategies for building new networks that aggregate water potential data across sites. We end by highlighting novel opportunities for linking more representative site-level observations of water potential to remotely sensed proxies. Together, these considerations offer a road map for clearer links between ecohydrological processes and the water potential gradients that have the 'potential' to substantially reduce conceptual and modelling uncertainties.

Gradients in the water potential ($Ψ$) of soils and plants form the energetic basis for the transport of water, and elements contained therein, through a connected continuum linking the deepest soil layers to the top of plant canopies (Fig. 1). The $Ψ$ can be a positive or negative pressure, although it is typically negative—a tension force—in unsaturated soils and within plant hydraulic systems. $Ψ$ gradients have been recognized as the fundamental driver of water fluxes between soils, streams and groundwater for more than a century, and they appear in some of the most foundational equations in hydrology<fnref n="1" /> (for example, Darcy’s Law and Richards’ Equation). Likewise, the critical role of $Ψ$ gradients in driving water flows through the soil–plant–atmosphere continuum has been known for decades².

Beyond redistributing water through ecosystems, $Ψ$ is also a direct control of many biophysical processes. Soil $Ψ$ ($Ψ_s$) regulates the flow of water into and out of soil microbe cells and determines their metabolism³. In plants, leaf $Ψ$ ($Ψ_l$) is a key driver of stomatal conductance and photosynthetic carbon uptake<fnref n="4" />,⁵, and its close connection to branch and stem $Ψ$ ($Ψ_s$) controls the risk of drought-driven xylem embolism and mortality⁶,⁷. Consequently, most ecosystem services, including water storage, food and fibre supply, and water and climate regulation, are fundamentally linked to $Ψ$.

While undeniably important for soil and plant function, for reasons that will be discussed in more detail, $Ψ_s$ is rarely measured in situ⁸,⁹, and observations of plant $Ψ$ have historically been limited to destructive and disjunct manual measurements. The objective of this paper is to demonstrate key uncertainties linked to the dearth of soil and plant $Ψ$ data and to discuss the theoretical and modelling progress that could be enabled with richer and more discoverable

information about $Ψ$. We begin by discussing issues surrounding the measurement, modelling and synthesis of $Ψ_s$ and then address additional considerations linked to the measurement and prediction of $Ψ$ in plants. We then present a road map for creating accessible and open $Ψ$ databases and discuss promising new approaches for detecting $Ψ$ using remote sensing.

## Concepts and uncertainties linked to $Ψ_s$

Water flows ‘downhill’ energetically, moving from areas of higher potential to areas of lower potential, such that $Ψ_s$ gradients are the driving force of subsurface water flows<fnref n="1" />. In most unsaturated soils, $Ψ_s$ is dominated by the matric potential, which becomes more negative when soils dry, and the effective radii of water-filled pore spaces in the soil become smaller. This process produces the general shape of the water-retention curve (also known as the ‘moisture characteristic’ or ‘water release’ curve), which relates $Ψ_s$ to volumetric soil moisture content ($θ$). Critically, variation in soil physical properties can cause $Ψ_s$ to differ by an order of magnitude across soil types, even if $θ$ is the same<fnref n="10" />,¹¹ (Fig. 2a).

Field observations of $θ$ are common¹², but with a few exceptions⁹,¹³, $Ψ_s$ is rarely measured systematically in field research settings⁸,⁹. The reasons why $θ$ became the predominant metric for describing soil water status are not entirely clear⁸, but may reflect the fact that no single instrument captures the entire range of $Ψ_s$ (from saturation to the very dry end), and sensors for measuring $Ψ_s$ in the field have historically been associated with unique limitations and uncertainty⁸,¹⁴.

Even if $Ψ_s$ data were plentiful, strategies for relating $θ$ to $Ψ_s$ would still be necessary in models to connect water-balance equations with

<footnote n="1">¹O'Neill School of Public and Environmental Affairs, Indiana University Bloomington, Bloomington, IN, USA. ²Department of Geography, Indiana University Bloomington, Bloomington, IN, USA. ³Department of Environmental Science, Policy, and Management, University of California Berkeley, Berkeley, CA, USA.</footnote>

<footnote n="4">⁴Department of Meteorology and Atmospheric Science and Earth and Environmental Systems Institute, The Pennsylvania State University, University Park, PA, USA. ⁵Life and Environmental Sciences Department, University of California Merced, Merced, CA, USA. ⁶Department of Earth System Science, Stanford University, Stanford, CA, USA. ⁷Laboratoire des Sciences du Climat et de l'Environnement, Paris, France. ⁸Southwest Watershed Research Center, USDA Agricultural Research Service, Tucson, AZ, USA. ⁹Department of Plant Science, The Pennsylvania State University, University Park, PA, USA.</footnote>

<footnote n="10">¹⁰Environmental Sciences Division, Oak Ridge National Laboratory, Oak Ridge, TN, USA. ¹¹School of Natural Resources, University of Missouri, Columbia, MO, USA. ¹²e-mail: knovick@indiana.edu</footnote>
<figure><img src="image_3.png" /><figcaption>**Fig. 1 | Ψ** links environmental drivers to biophysical responses. Water flows downhill along gradients of Ψ in the soils (Ψs, where Ψ is relatively high, often >−1 MPa) through the stems (Ψs) to the leaves (ΨL, where potential is relatively low) and eventually to the air (Ψair, where it can be as low as −100 MPa). Ψ also directly controls key biological processes, including microbial function, mortality risk arising from damaged plant xylem, and plant-atmosphere gas exchange. While observations of environmental drivers, θ, and carbon and water fluxes are broadly accessible from environmental networks and remote sensing, Ψ time series are more discrete, sparse and generally not coordinated or discoverable.</figcaption></figure>

potential-driven flows. Most hydrologic and land-surface models thus rely on water-retention-curve models¹⁵, with those proposed by refs. ¹⁰,¹¹ ranking high in popularity. Pedotransfer functions (PTFs) predict the parameters of water-retention-curve models using empirical equations driven by a limited set of soil characteristics (typically %sand, %clay and bulk density¹⁶⁻¹⁸).

While developing PTFs is an active field¹⁵, PTF parameter distributions are poorly constrained and prevent confident transformation of θ to Ψs. For example, even relatively small variations in a single parameter of the van Genuchten model¹¹ cause Ψs to vary by an order of magnitude over a wide range of θ (Fig. 2b–d). Soil structure, which differs from soil texture and is governed by biophysical properties, may be a key omission in PTFs¹⁹ explaining some of this uncertainty. For example, growth of roots and mycorrhizae into soil pores, and deposition of root exudates, increase overall water retention²⁰,²¹, and macropores can create preferred flow pathways that are challenging to incorporate into PTFs. Moreover, depth into the soil may also affect hydraulic properties by controlling connectivity with root systems and through slowly evolving changes in soil morphology. Finally, most PTFs assume that the water-retention curve is static, but many relevant processes occurring in natural landscapes (including drying-rewetting cycles, fire, and management shifts) may cause time-dependent hysteresis of the water-retention curve²²⁻²⁴.

This uncertainly linked to PTFs propagates through water-cycle models in highly consequential ways.²⁵,²⁶ Previous work performed in the Shale Hills Critical Zone Observatory confirms that van Genuchten model¹¹ parameters are the dominant source of model uncertainty in a coupled three-dimensional (3D) land-surface and hydrological model²⁷, and that water-retention-curve parameters must be measured locally and optimized through data assimilation²⁸ for watershed hydrologic variables to be predicted with any degree

of certainty²⁹. Here, using a popular 1D water-balance model, we further demonstrate that uncertainty in a single PTF parameter drives large uncertainty in modelled predictions of evapotranspiration, soil moisture and Ψs (Fig. 2e).

The parameters of the water-retention curve are also key sources of uncertainty explaining variability in carbon cycle fluxes from global-scale land-surface models. In this study, we used a global sensitivity experiment³⁰ to explore the variability of these parameters along with other key parameters of the ORCHIDEE land-surface model³¹,³² (see Methods for details). The parameters of the water-retention curve explained between 10% and 32% of the modelled GPP variance across three diverse sites (Fig. 3). Moreover, when considering the wider set of soil hydrology parameters (including the hydraulic conductivity, field capacity and permanent wilting point of the soil), the percentage of explained GPP variance increased to 22–53% across sites.

The dearth of information about Ψs is not only a problem for models, but also confounds observation-driven work. Because θ is widely measured, and Ψs is not, it is extremely common to see key response variables such as carbon and water fluxes explained as a function of measured θ³³⁻³⁵. These relationships are usually nonlinear and threshold driven³⁶,³⁷. This is not surprising, as these responses embed site-to-site variability in the water-retention curve, which itself is nonlinear and threshold driven (Fig. 2a–d). The shape of these response functions thus depends very much on whether Ψs or θ is chosen as the driving variable³⁸. Indeed, the relationship between gross primary productivity (GPP) and soil water status is more linear and less spatially heterogeneous when Ψs, as opposed to θ, appears on the x axis (Fig. 4). Likewise, substantial skill in predicting soil respiration can be gained when model functions are driven explicitly by Ψs (ref. ³). Thus, more abundant and aggregated site-level Ψs information could reduce conceptual
<figure><img src="image_4.png" /></figure>

**Fig. 2** | Water-retention curve and PTF uncertainty. **a.** Across three soil types, $Ψ_s$ can differ by an order of magnitude for a given $θ$ (with curves generated from the van Genuchten model$^{11}$, see Methods). **b–d.** The uncertainty in the water-retention curve attributable to PTF parameter uncertainty. The shaded area shows the 90% confidence interval due solely to variation in a single parameter of the van Genuchten model (the *n* shape parameter, which is linked to pore size) within just one standard deviation of its reported distribution for each soil class from a popular PTF$^{18}$: silty clay (**b**), silt (**c**) and loamy sand (**d**). Thick lines in **b–d** are the same as in **a**. The PTF-driven uncertainty in the water-retention curve propagates into large uncertainty for modelled fluxes and pools. **e–g.** Specifically, variation in the van Genuchten *n* parameter within again just one standard deviation of its reported range$^{18}$ causes the 90% confidence intervals on modelled evapotranspiration (ET) (**e**), $θ$ (**f**) and $Ψ_s$ (**g**) (shaded grey areas) to vary by a magnitude comparable to the mean value of each parameter (thick black line). Simulations were run using the HYDRUS 1D$^{79}$ model for a forest site in Indiana, USA$^{80}$, during a drought event (see Methods for details).

uncertainty about how ecosystem fluxes respond to soil water defi-
cits and permit other sources of spatio-temporal variability to be
more discernable.

**Plant Ψ: key concepts and controversies**

The effective radii of evaporating water surfaces within plant cell walls are extremely small, resulting in tension forces strong enough to pull water upwards from soils, where it is already tightly bound, to the leaves. Thus, the difference between $Ψ_L$ and $Ψ_S$ is the driving force for transpiration, which is closely coupled with photosynthetic carbon uptake. Moreover, $Ψ_X$, which is coupled with $Ψ_L$, interacts with anatomical features of the plant's water transport system to determine the risk of xylem embolism that can lead to mortality$^{6,7,39–41}$. Stomatal regulation of gas exchange is also critical for buffering plants from the very low $Ψ$ of the atmosphere (see Fig. 1), which is extremely sensitive to relative humidity$^{42}$.

Historically, observations of plant Ψ have been limited to manu-
ally collected 'snapshots' (for example, with a pressure chamber<sup>43</sup>).
These data have proved indispensable for shaping our theoreti-
cal understanding of how plants respond to soil water stress<sup>6,7,40,44</sup>.
However, because pressure-chamber measurements are destructive
and labour intensive, they are typically limited to weekly or seasonal
temporal resolutions. While the weekly timescale is well matched to
soil drying, it is too coarse to capture faster-acting hydrodynamic
processes, including stomatal response to vapour pressure deficit
(VPD<sup>45</sup>) and the depletion and refilling of plant water pools over
the course of a day<sup>46</sup>. Moreover, with some exceptions<sup>47</sup>, $Ψ_L$ and $Ψ_X$
are not often monitored over long periods (for example, years to
decades), and centralized databases and networks for time series of
Ψ do not yet exist.

The discrete and undiscoverable nature of plant Ψ observations
limits our ability to characterize the distributions of the mini-
mum plant Ψ that are so critical for determining plant mortality
risk⁴¹. The gap also limits understanding of how plant Ψ and Ψₛ are

coordinated and coupled. For example, a fundamental assump-
tion in plant eco-physiology is that $Ψ_L$ and $Ψ_X$ are equilibrated with
$Ψ_S$ across the root zone in pre-dawn hours⁴⁸. This assumption has
allowed eco-physiologists to circumvent the $Ψ_S$ data scarcity prob-
lem by relying on pre-dawn $Ψ_L$ observations as a proxy for root-zone
$Ψ_S$—an approach that treats the plants as an instrument for record-
ing the soil water environment. Yet experiments have shown that
night-time transpiration—while small—can still occur¹⁹,⁵⁰, lowering
pre-dawn $Ψ_L$ and decoupling it from $Ψ_S$ (ref. ⁵¹). Synthetic assess-
ments of pre-dawn equilibrium are hindered by the absence of
nocturnal $Ψ_L$ observations collected together with data on $Ψ_S$ and/
or stem water flows (for example, from sap flux), or collected fre-
quently enough to determine whether stationarity in pre-dawn $Ψ_L$,
which should be a hallmark of equilibrium, has been achieved.

Likewise, the Ψ information gap limits understanding of how $Ψ_S$ and plant Ψ are coupled at mid-day. The relationship between mid-day $Ψ_L$ and the root-zone $Ψ_S$ is frequently used to classify plant water-use strategies$^{44,52,53}$. For example, plants with conservative water-use strategies ('isohydric' species) close stomata quickly as $Ψ_S$ declines, whereas 'anisohydric' plants keep stomata open longer, sustaining gas exchange but with more rapid declines in $Ψ_L$ that may increase the risk of xylem embolism. The (an)isohydric framework is popular but controversial, with several studies highlighting critical interactions with other environmental drivers beyond $Ψ_S$ (refs. ⁵⁴⁻⁵⁶), including VPD⁵⁷. Moreover, coordinated observations of sap flow, enhanced with data on $Ψ_S$ and $Ψ_X$, hold great promise for understanding how the dynamics of hydraulic conductance of different plant organs influence whole-plant hydraulic physiology⁵⁸. Plant hydraulics schemes relying on concepts such as isohydrity are rapidly being incorporated in hydrologic and Earth system models⁵⁹⁻⁶¹. Benchmarking and testing these schemes would benefit from open and spatially representative databases of plant Ψ and $Ψ_S$ time series, measured together at a temporal frequency (for example, hourly) over which key drivers such as VPD vary.
<figure><img src="image_5.png" /><figcaption>**Fig. 3** | Water-retention-curve parameters are a key source of land-surface model uncertainty. A sensitivity analysis of key model parameters of the ORCHIDEE land-surface model<sup>31,32</sup> was performed to demonstrate the relative importance of each parameter in simulating daily GPP at three contrasting FLUXNET sites. **a.** A temperate broadleaf forest (Harvard Forest, FLUXNET code US-Ha1<sup>85</sup>). **b.** A boreal needleleaf forest (Sodankyla, FI-Sod,<sup>82</sup>). **c.** A semi-arid savannah (Damokeya, SD-Dem<sup>83</sup>). The Sobol method<sup>30</sup> was used to perform the sensitivity analysis; this method is based on variance decomposition and is able to capture interactions between parameters. More details can be found in Methods.</figcaption></figure>

Coordinated observation of plant $Ψ$ and $Ψ_s$ could also offer new perspectives on the critical role of root hydraulic function. Pre-dawn observations of $Ψ_L$ and $Ψ_L$ from multiple depths could reveal interspecific patterns in functional rooting depth—a trait that is difficult to measure by other means and partially responsible for model difficulty in capturing plant drought responses<sup>62</sup>. When complemented with data on $Ψ_x$ and/or root sap flow, profile observations of $Ψ_s$ would also illuminate the important but poorly understood consequences of hydraulic redistribution of water from wetter to drier soil layers through plant roots<sup>63,64</sup>. While root $Ψ_x$ is difficult to measure with pressure chambers, it could be monitored more easily with psychrometers or other techniques for continuous observation of plant $Ψ_x$. Data on root $Ψ_x$, especially when paired with laboratory-derived root xylem vulnerability curves, would also be useful for understanding the dynamics of root hydraulic conductance, noting that roots may be among the most vulnerable components of the plant hydraulic system<sup>65,66</sup>. Finally, differences in $Ψ_s$ and root $Ψ_x$ could also improve our understanding of gradients in $Ψ$ occurring at the root-soil interface<sup>67</sup>.

## Strategies to address the Ψ information gap

Recent advances in measurement technology have substantially improved the ease and reliability of $Ψ_s$ observations. In the lab, sensor improvement has reduced the time necessary to generate the 'wet end' of the water-retention curve<sup>68</sup>. A second instrument, typically a dew-point potentiometer, is required to capture the dry end of the curve, but this step proceeds relatively quickly. While the instrumentation and expertise necessary to characterize water-retention curves may be siloed within soil science disciplines, this barrier could be easily overcome through cooperative arrangements and/or knowledge transfer. At the same time, technology is improving for more confident observation of $Ψ_s$ in situ<sup>8</sup>. Tensiometers, which are accurate when soil is relatively wet (for example, $Ψ_s > -0.1$ MPa),

are widely used in agricultural settings for the purposes of irrigation scheduling. In the drier range, soil matric potential can be measured using psychrometry or from dielectric measurements, with several commercial sensors available at a relatively low cost (for example, the Teros 21 product, Meter Group). While the accuracy of sensors such as these is greatest when $Ψ_s$ is above -2 MPa, this is still lower than the wilting point of many plant species<sup>8</sup>.

With respect to plants, psychrometers permitting continuous and long-term observation of both $Ψ_L$ and $Ψ_x$ are becoming more widely and commercially available (for example, the PSY1 products, ICT International), drawing from a long history of psychrometric approaches for measuring plant $Ψ$ (ref. <sup>65</sup>). Stem psychrometers can now be deployed on branches and boles of some species for weeks to months at a time<sup>55</sup>, and evidence is mounting that high-frequency $Ψ_L$ and $Ψ_x$ data can indeed improve our understanding of plant water-use strategies and dynamics<sup>55,70</sup>. Psychrometers are still relatively expensive, best suited for broadleaf and non-resinous species and sensitive to biases linked to temperature fluctuations and wounding effects. Thus, for now, psychrometer data are best viewed as complementary to pressure-chamber measurements. Nonetheless, for many plants, these instruments allow for the collection of $Ψ_L$ and/or $Ψ_x$ data at the hourly timescales necessary to be harmonized with observed carbon and water fluxes (for example, from sap flux and flux towers) and to more rigorously test model frameworks.

Ultimately, addressing environmental questions at policy- and management-relevant scales requires the collection and standardization of observations across many sites. This need has motivated the recent development of many environmental observation networks, including highly centralized initiatives such as the National Science Foundation's National Ecological Observatory Network<sup>71</sup>, as well as more bottom-up networks such as AmeriFlux<sup>72</sup> and FLUXNET<sup>73</sup> and the new international SAPFLUXNET network<sup>74</sup>. Other approaches include 'network-of-networks' cyberinfrastructure such as the International Soil Moisture Network,<sup>13</sup> which aggregates soil moisture observations from dozens of individual networks.

Both bottom-up and top-down approaches could be useful for building new $Ψ$ networks. On the one hand, centralized and standardized deployment of new $Ψ$ sensors, ideally in locations that are already nodes of other networks, would have the advantage of uniformity in instrumentation and data quality control that facilitates cross-site synthesis. On the other hand, a community-driven effort to aggregate and redistribute both existing and new $Ψ$ data could follow the highly successful 'coalition' model employed by networks such as AmeriFlux<sup>72</sup>, increasing the discoverability of data while allowing room for innovation at the site level. Even a concerted effort to generate and/or collect laboratory-based water-retention curves from existing network sites could substantially constrain how much of the nonlinearity in the response of fluxes to observed soil water content can be explained by soil physics (for example, see Fig. 4). The success of a $Ψ$ network would be maximized with (1) a focus on collecting data from sites that also support continuous plant- and/or stand-scale carbon and water fluxes, (2) cyberinfrastructure to support the discoverability and distribution of these databases, (3) a focus in at least some locations on within-site spatial heterogeneity in $Ψ$ dynamics to better understand how many observation points (and at what depths) are necessary to substantially improve model skill, and (4) training programmes, such as summer short courses or distributed graduate seminars, to transfer knowledge about how to interpret network observations and to share best practices for sensor deployment.

Even with well-developed observation networks, it is not possible to measure key physiological variables such as $Ψ$ everywhere and all the time. Thus, strategies for linking these variables to proxies observable from space are required for regional- and
<figure><img src="image_6.png" /><figcaption>**Fig. 4** | $Ψ_S$ better explains variability in GPP when compared with $θ$. **a–j**, The relationship between GPP (normalized by its well-watered rate) and $Ψ_S$ (**f–j**) is more linear than the relationship between GPP and $θ$ (**a–e**) across four AmeriFlux sites for which site-specific water-retention curves were measured$^{38,84–86}$: a temperate broadleaf forest (US-MMS) (**a,f**), a semi-arid woody savannah (US-SRM) (**b,g**), a woody savannah (US-TON) (**c,h**), another temperate broadleaf forest (US-MOz) (**d,i**), and all together (**e,j**). Moreover, cross-site heterogeneity in the response functions is reduced when it is $Ψ_S$, as opposed to $θ$, on the x axis (compare **e** with **j**). GPP estimates were obtained from AmeriFlux, with site codes given in parentheses. Error bars indicate one standard error of the mean, which is quite small for some of the binned averages. See Methods for more details.</figcaption></figure>

continental-scale work, with microwave remote sensing represent-
ing a particularly promising approach. Microwave observations can
be used to determine vegetation optical depth (VOD), which is sen-
sitive to plant water content$^{75}$ and should be monotonically related
to $Ψ_L^{76,77}$. Comparison of observed $Ψ_L$ with either space-borne$^{78}$ or
tower-based$^{70}$ radiometry confirms that VOD and $Ψ_L$ follow similar
dynamics, especially after accounting for the effect of changing bio-
mass and leaf area. However, the exact relationship between VOD
and $Ψ_L$ is influenced by vegetation type$^{76}$, and further study of this
relationship is currently hindered by the sparsity of $Ψ_L$ data.

Importantly, microwave remote-sensing observations can be
made at night, which raises the question of whether nocturnal
microwave remote sensing of $Ψ_L$ can be used to infer dynamics of
root-zone $Ψ_S$. Answering this question requires a critical under-
standing of when and where pre-dawn $Ψ_L$ is equilibrated with
root-zone $Ψ_S$. This knowledge gap can be addressed with network
observations of $Ψ_L$ from psychrometry or observations of plant $Ψ$
and $Ψ_S$ collected in the same site, which could then guide the design
and interpretation of both tower- and satellite-mounted microwave
remote-sensing systems. The approach will also require further
refinement of retrieval algorithms for separating the contribution
of plant and soil water content, for example, by leveraging emerging
approaches for the remote sensing of vegetation structure$^{77}$.

In conclusion, we have highlighted how more numerous, discov-
erable and continuous observations of $Ψ_S$ and plant $Ψ$ can not only
improve our conceptual understanding of biophysical processes
throughout the soil–plant–atmosphere continuum, but also serve as
a much-needed new tool for benchmarking and calibrating hydro-
logic and land-surface models and remote-sensing products. While
in situ and site-specific observations of $Ψ_S$, $Ψ_L$ and $Ψ_S$ may not yet
be easy, recent advancements in sensor technology have certainly

made them easier than in decades past. The time is right for a new
focus on the collection of these data in the field and the develop-
ment of new networks to aggregate observations across sites com-
plemented by new approaches for integrating these observations
into Earth system models.

Online content

Any methods, additional references, Nature Research reporting summaries, source data, statements of data availability and associated accession codes are available at [https://doi.org/10.1038/s41561-022-00909-2].

Received: 1 April 2021; Accepted: 2 February 2022;
Published online: 11 March 2022

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## Methods

**Water-retention-curve uncertainty.** The water-retention curves in Fig. 2 were created using the van Genuchten water-retention curve model<sup>11</sup> relating $Ψ_s$ to $θ$. As described in more detail in the Supplementary Information, most parameters of the model were held constant within each soil type, specified as the mean values reported in the updated ROSETTA PTF<sup>18</sup> (Supplementary Table 1). The 'n' parameter—a key shape parameter of the van Genuchten model—was allowed to vary by randomly selecting a value from a uniform distribution bounded by ±1 standard deviation as reported for the ROSETTA PTF<sup>18</sup>. Overall, this was a conservative approach; drawing the values of *n* from the full distribution reported for each soil type expands the range of predicted $Ψ_s$ by orders of magnitude.

**The HYDRUS 1D simulations.** Uncertainty in the water-retention curve linked to pedotransfer uncertainty (for example, as Fig. 2a–d) was propagated through predictions of $Ψ_s$ and $θ$ (at depths of 15 cm) and surface evapotranspiration (cm d<sup>-1</sup>) using the HYDRUS 1D soil water-dynamics model<sup>79</sup>. Fifty simulations were performed for the Bradford Woods deciduous forest site in south-central Indiana, where the HYDRUS 1D model had been previously calibrated<sup>80</sup>. In general, model settings were left unchanged, with a few exceptions as discussed in more detail in the Supplementary Information. The soil at Bradford Woods is characterized by a 40-cm-depth AP (plowed A) horizon dominated by sandy loam and a BW (weathered B) horizon dominated by silt loam from a depth of 40 cm to 208 cm. The very bottom of the soil layer (depths 208–230 cm) was prescribed to be clay loam. The parameters of the van Genuchten model used in the HYDRUS simulations are shown in Supplementary Table 2, where again most were held constant, but *n* varied for the sandy and silt loam layers by drawing it from within one standard deviation of its distribution reported in the updated ROSETTA PTF<sup>18</sup>. The shaded areas in Fig. 2e,f thus illustrate the resulting variations in evapotranspiration, $Ψ_s$ and $θ$ due solely to variability in *n*.

**The ORCHIDEE GPP sensitivity analysis.** The ORCHIDEE land surface model (CMIP6 version)<sup>31,32</sup>, which is the terrestrial part of the IPSL (Institute Pierre-Simon Laplace) Earth system model, was used to explore the sensitivity of modelled GPP to uncertainty in a wide range of parameters. ORCHIDEE relies on the van Genuchten model to calculate $Ψ_s$ as well as the hydraulic conductivity and diffusivity required to solve the Richard's diffusion equation. ORCHIDEE discretizes the first 2 m of the soil column over 11 layers. For this experiment, we ran ORCHIDEE over three single-mesh locations using local half-hourly forcing data to drive the model at each site (Supplementary Table 3) and considered modelled GPP at a daily time step. The sensitivity analysis results shown in Fig. 3 were generated using Sobol's method<sup>30</sup>, using the SALib python package<sup>87</sup> to sample the parameter space and execute the algorithms. Briefly, the model was run using different parameter ensembles, with parameters varied within their reported ranges of uncertainty. Then, each modelled GPP time series was compared with GPP derived from flux-tower observations. The variance of simulated GPP was then decomposed into fractions that can be attributed to each parameter tested. These results, shown in Fig. 3, capture both independent and interactive contributions of each parameter to the total variance. When interactions are removed, the independent contribution of water-retention-curve parameters is still significant, and actually increases for the semi-arid site (see details in Supplementary Information section 3).

**The AmeriFlux GPP analysis.** Half-hourly or hourly data from the four flux towers referenced in Fig. 4 were acquired from the AmeriFlux network (ameriflux.lbl.gov) and subjected to standardized quality-control, gap-filling, and partitioning approaches. The sites and quality-control procedures are described in more detail in Supplementary Table 5. The methods used to determine the relationship between GPP and soil moisture are similar to those previously used to explore the relationship between surface conductance and soil moisture<sup>35</sup>. Briefly, analysis was constrained to the peak of the growing season to limit bias linked to phenological variation in leaf area index. Estimates of $Ψ_s$ for each site were determined from

site-specific water-retention curves<sup>38,81–83</sup>. The data were then sorted into eight bins representing the 15th, 30th, 45th, 60th, 70th, 80th, 90th and 100th quantiles of the observed values of soil moisture content in each site. Within each bin, data were constrained to relatively high light (net radiation >300 W m<sup>-2</sup>) conditions with VPD limited to $1 \le VPD \le 1.5$ kPa in US-MMS, US-TON and US-MOz and $1.5 \le VPD \le 2$ kPa in the more arid US-SRM site. The mean GPP, $Ψ_s$ and $θ$ were then calculated for each bin using the filtered data and normalized by the maximum bin-averaged value observed at each site.

## Data availability

The FLUXNET tower data appearing in Fig. 3 are from the FLUXNET 2015 dataset (https://doi.org/10.18140/FLX/1440186 for SD-Dem, https://doi.org/10.18140/FLX/1440071 for US-HA1 and https://doi.org/10.18140/FLX/1440160 for FI-SOD). The AmeriFlux tower data appearing in Fig. 4 are available from the AmeriFlux network (https://doi.org/10.17190/AMF/1246080 for US-MMS, https://doi.org/10.17190/AMF/1246081 for US-MOz, https://doi.org/10.17190/AMF/1246104 for US-SRM and https://doi.org/10.17190/AMF/1245971 for US-TON).

## Code availability

The HYDRUS 1D programme used to create the results of Fig. 2e–g is available for public download from https://www.pc-progress.com/en/Default.aspx?hydrus-1d. A reference version of the ORCHIDEE land-surface model, used for Fig. 3, is available at https://orchidee.ipsl.fr/. Details on the parameterizations of these models are presented in the Supplementary Information.

## References

87. Herman, J. & Usher, W. SALib: an open-source Python library for sensitivity analysis. *J. Open Source Softw.* https://doi.org/10.21105/joss.00097 (2017).

## Acknowledgements

K.A.N. acknowledges support from NSF (DEB, grant 1552747) and the AmeriFlux Management Project via the US Department of Energy, Office of Science Lawrence Berkeley National Laboratory. A.G.K. was supported by NASA Terrestrial Ecology (award 80NSSC18K0715). J.D.W. acknowledges support from the US Department of Energy, Office of Science, through Oak Ridge National Laboratory's Terrestrial Ecosystem Science Focus Area. K.J.D. and Y.S. were supported by National Science Foundation grant EAR 1331726 (S. Brantley) for the Susquehanna Shale Hills Critical Zone Observatory.

## Author contributions

K.A.N. conceived of the study with substantial input from D.L.F., A.G.K., K.J.D., T.A.G., R.L.S., B.N.S., Y.S. and N.M. Data analyses were performed by K.A.N., T.A.G., D.L.F. and N.R., who also created the resulting figures. D.B., R.L.S., K.A.N. and J.D.W. contributed AmeriFlux data used in Fig. 4. All authors wrote the text and provided substantial conceptual input to the manuscript.

## Competing interests

The authors declare no competing interests.

## Additional information

**Supplementary information** The online version contains supplementary material available at https://doi.org/10.1038/s41561-022-00909-2.

**Correspondence** should be addressed to Kimberly A. Novick.

**Peer review information** *Nature Geoscience* thanks Christopher Still, Vincent Humphrey and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

**Reprints and permissions information** is available at www.nature.com/reprints.