The Tyranny of Small Scales—On Representing Soil Processes in Global Land Surface Models – Or – 2020 – Water Resources Research


1 Introduction

I am deeply honored by the recognition of delivering the 2018 Walter B. Langbein lecture. It is humbling and thrilling to join the ranks of previous distinguished Langbein lecturers. The significance of this recognition and the opportunity to communicate a message clearly resonates from their inspiring lectures and universal wisdom. (I urge you to view some of these online at the AGU’s website.) To my embarrassment, I had only a vague notion of Walter Langbein’s many contributions, mostly from previous Langbein lectures. The more I delved into the fascinating history of Langbein’s career, the more I became impressed by his prolific and diverse scientific contributions and by his personality and lifelong service to building a modern and scientifically based hydrology community. This has been a gratifying journey of discovery into the life and contributions of this humble giant of hydrology.

In the main goal of this perspective paper is to present some of the key challenges and experiences of transitioning from the study of soil and hydrologic processes at the sample or profile (pedon) scales to the consideration of the effects and emergent behaviors at regional and global scales relevant to climate. I first review several fascinating historical aspects of land‐surface representation originally conceived for weather prediction and dating back to the seminal work of Richardson (1922). Before the advent of modern day global‐scale surface process representation, hydrology struggled with a long‐standing challenge of small‐scale process representation at the watershed scale. The large gap between sample and watershed scales and the reliance on small‐scale parameterization and physical laws are in the core the debate and sometimes frustration with what has been perceived as the tyranny of small scales. We will focus on the state of soil surface representation in large‐scale models and trace the origins of soil information with the dominance of arable land information in the record. Next, we leap to the global scale and largely bypass unresolved small scales to capitalizing on coarse representation where details of the underlying processes become less important (especially for pixels of many kilometer in size). A new class of large‐scale phenomena emerge and shed new light on hydrologic and climatic behaviors of catchments (albeit averaged in space and time). Global maps of soil properties are used to infer pedotransfer functions (PTFs) that link soil hydraulic properties (SHPs) with easy‐to‐measure attributes and provide parameters for hydrological and Earth System Models. The direct links between small‐scale properties and global‐scale applications of SHP have been extended to other physical processes such as surface resistance to evaporation, infiltration behavior, and unsaturated flow and transport based on the Richards equation. The effective representation of surface processes at global scale remains a daunting task primarily due to dominance of small scales (i.e., sample scale measurements and physics). Recent advances seem to focus on practical and incremental improvements rather than seeking a rigorous and formal reconciliation of scales, for example, by gradual improvement of PTF parametrization with the addition of physical constraints, flux matching formalism (Samaniego et al., 2017), by directly incorporating effects of vegetation and soil structure and migrating small‐scale physics and process representation for global flux partitioning (improving available physical frameworks). An important development of the last decade is the availability of spatially resolved and continuous data that open new possibilities using large‐scale system responses to constrain parameters, to address heterogeneity and to improve model selection and structure (Chaney et al., 2018; Clark et al., 2017; Mizukami et al., 2017; Zhang et al., 2010).

1.1 Soil Representation and Numerical Weather Prediction

The journey takes us back a100 years ago at the end of the First World War (around the time the AGU was founded in 1919). Lewis Fry Richardson (Figure 1a) was 37 years old when he returned from the war where he served with Friends’ Ambulance Unit transferring wounded from the battle lines. (He was a Quaker and an ardent pacifist, and as a contentious objector, he was exempt from regular military service) In the pauses between battles, he completed a manuscript he has been working on for a few years on “Weather Predication by Numerical Process”. The manuscript was sent back from the front lines to be lost and then accidently found and subsequently published in 1922. Among the numerous theoretical and practical topics that Richardson had to resolve was the challenge of land surface representation with water and hear fluxes at the soil surface (and into the soil). This recognition of the importance of soil surface fluxes, led Richardson to derive what is now known as the Richards equation in 1917, more than a decade before L. A. Richards published his work in 1931 (see Figure 1c). Richardson’s work is inspiring not only by his foresight that paved the way for modern numerical modeling of weather and climate but also for the early recognition of the links between near surface hydrologic processes and climate models. He was a pioneer that established the framework for coupling surface, subsurface, and atmospheric processes from the very beginning of numerical weather modeling.

(a) Lewis Fry Richardson (1881–1953), (b) Richardson’s map of weather stations and landscape grid for pressure (dark) and velocity (white) calculations: frontispiece of Weather Prediction by Numerical Process (Cambridge University, 1922), and (c) the Richardson‐Richards equation for unsaturated capillary flow in soil.

1.2 Small‐Scale Processes in Watershed Hydrology

Before considering soil surface representation at global Earth System models, it is instructive to revisit a long‐standing challenge of small‐scale process representation at the intermediate scales of catchment hydrology. The challenge of small‐scale parameterization and process representation has dominated the hydrological discussion for the past few decades. From an initial enthusiasm and adoption of a blueprint for distributed hydrological numerical modeling (Freeze & Harlan, 1969), the discussion quickly centered on limitations and inadequacies of such an approach (Beven, 2001; Dooge, 1986; Klemes, 1983; McDonnell et al., 2007; Sivapalan, 2018; Wood, 1995 and others). New opportunities presented by large data with the need for rigorous model selection and hypotheses testing (Clark et al., 2017) make it clear that catchment scale hydrologic modeling under the “business as usual” mode is no longer viable, and a paradigm shift is needed. In the absence of a framework for advancing such paradigm change, we are faced with a pragmatic dilemma regarding how much efforts should be invested in resolving the watershed scale representation. In the core of this long‐standing challenge are three interlinked issues:

  1. the prohibitive task of small‐scale parameterization of large and heterogeneous hydrologic systems;
  2. small‐scale physics may not represent processes at large scales; and
  3. overparameterization and complex model structure preclude credible testing.

The tyranny of small‐scale representation seems to have created an impasse.

Beven in his 2001 Dalton lecture “How far can we go in distributed hydrological modelling?” made the following observation: “It is clear that we have kept the Richards equation approach as a subgrid scale parameterisation for so long because it is consistent with measurement scales of soil physical measurements we have not developed the equivalent, scale consistent, process descriptions that would then take account implicitly of the effects of subgrid scale heterogeneity and nonlinearity .” The situation has not changed much since then. Beven (2001) listed additional critical issues related to the challenges of heterogeneity, uncertainty, parameter equifinality that complement Klemes (1983) and Dooge (1986) in their quest for unifying laws and ways for addressing the challenge of scales in hydrology (see also a review by Blöschl & Sivapalan, 1995). A young hydrologist reflecting on these learned discussions may be under the impression that the field is in an apparent conceptual stagnation. Although aspects of uncertainty, equifinality, heterogeneity, systematic hypothesis testing, model structure, and scale‐appropriate parameterization remain largely unresolved; nevertheless, progress occurs everywhere in different and unexpected ways, for example, with the advent of global scale Earth system models that benefit from unprecedented detailed observations (Chaney et al., 2018; Zhang et al., 2010), or stronger integration with ecological and climate models, the development of continental scale surface and groundwater models and more. These developments seem to fulfill Klemes (1983) prophetic vision regarding leap of scales: “Hydrology will jump ahead after its links with processes at the planetary level are better established, in a similar way as advances in chemistry were made possible by developments in atomic physics. This belief stems from an observation that a successful solution of a problem is more likely if it is approached from two opposite directions. In hydrology, the ‘other’ direction is ‘downwards’ from global concepts .” In the past decade, the hydrology community has gradually embraced approaches that skip many scales (inspired by global climate models) and circumvent the impasse of small scales. Yet, small scale processes are not abandoned; the community continues to make advances from the “other direction” as well. Next, we discuss ingredients of this promising pragmatic approach.

1.3 From Richardson to Dokuchaev—Soil Surveys and Pedotransfer Functions

An important ingredient for large‐scale hydroclimatic modeling is land surface parameterization (Richardson, 1922), specifically soil attributes and hydraulic properties. The general practice uses maps of soil types based primarily on soil texture (with supplemental information on soil organic matter, density, horizons, etc.) and correlates these properties with hydraulic, thermal, and other properties of the soil required for large‐scale models. The information used for soil property mapping accumulated primarily from systematic soil surveys dating back to the late nineteenth century to Dokuchaev in Russia (1883) and the inception of soil survey in the USA by an act of Congress in 1896 (Div. of agricultural soils at United States Department of Agriculture (USDA) headed by Milton Whitney, since 1894). The original motivation was to assist farmers with understanding their soils and improve land‐use practices and for taxation purposes in Europe (Brevik et al., 2016). Scientifically based national surveys of agricultural lands became common in the early twentieth century following the rapid expansion of agriculture and improved understanding of soil properties and their classification (national soil surveys in Canada, India, China, Australia, and other countries). Some of the national soil survey databases were merged to create present day global soil maps (e.g., Harmonized World Soil Database and SoilGrids, FAO/IIASA/ISRIC/ISS‐CAS/JRC, 2012) by reconciling profile information, using supplemental remote sensing information and advanced machine learning methods. For example, the creation of the SoilGrids250m uses 150,000 soil profiles for training advanced machine learning and spatial interpolation (Hengl et al., 2017). Despite the remarkable progress in providing detailed soil maps for modeling, we must bear in mind their origins in soil surveys of arable lands that represent only 10% of the land surface.

It is reasonable to suspect the dominance of arable land in global soil maps to play a role in the observed bias in soil textural classes toward agricultural loamy textural classes. There are additional factors at play, such as a pronounced textural class smoothing by interpolation methods that converge to mean textural class—loam (results not shown). However, a more important bias in presently used soil texture‐based information is the lack of soil structure representation. This important soil attribute is expected to affect hydrologic and ecological responses, especially the partitioning of surface fluxes due to biopores and interaggregate pore spaces not considered in soil texture information. These two soil factors (textural “loamification” and lack of soil structure) are likely to propagate into inferences of soil hydraulic properties based on PTFs that rely heavily on soil texture information (Gutmann & Small, 2007; Looy et al., 2017). PTFs are used to correlate easy‐to‐measure soil properties (largely texture) with more difficult to measure soil hydraulic functions (and other properties). The methods used for deriving modern PTFs include statistical regression, neural networks, and lookup tables. The resulting correlations rely on a very small sets of soil hydraulic measurements (probably <10,000), most of which are based on laboratory‐measured values; use small soil volumes or samples that are not uniformly distributed over the land surface (many come from arable lands). It is important to recognize the limited and biased nature of soil information in the basis of neural networks or regression relations for the SHP used to represent the Earth’s land surface.

1.4 Limitations of Pedotransfer Functions and Practical Solutions

It comes as no surprise that SHP exhibit large scatter as illustrated by Gutmann and Small (2007) or Fatichi et al. (2020). Considering soil samples with a similar texture but unaccounted for influences of soil structure, we should expect large scatter in the resulting SHP. In their study, Gutmann and Small (2007) have shown that across a range of vegetation covers and climates, soil textural classes explain only 5% of the variance expected from the real distribution of SHP. In other words, parameter variations exceed expected differences due to soil texture classification. Land surface modelers and hydrologists have long recognized these limitations and, in the absence of systematic frameworks for better soil representation, have opted for ad hoc tuning of SPH values to improve model performance (e.g., with respect to runoff or evaporation). The problem is that while empirical tuning may offer a practical relief in the short term, it creates liability in the long term due to reluctance of modelers to embrace new soil information updates as they become available (due to concerns over potential adverse impacts on model performance). This dilemma highlights the long‐term advantage of using systematic and physically based approaches for determining SHP (and other parameters) with minimal empiricism and tuning (even at the cost of an initially reduced model performance).

To address the omission of soil structure in PTF‐SHP and potential effects of biopores and macroporosity on surface fluxes, Fatichi et al. (2020) performed a systematic study of soil structure effects using data from 20 representative locations. They evaluated the ecohydrologic responses for each site with and without soil structure considerations using an ecosystem model (T&C; Fatichi et al., 2012). Soil structure information was injected into the SHP by adjusting the saturated hydraulic conductivity only to account for activation of soil macropores during certain rainfall events. The adjustment reflects soil modification due to biological activity at a location that was associated with vegetation attributes (gross primary production or leaf area index as surrogates). A tacit assumption is made that biological formation of soil structure is directly linked with the amount of vegetation cover and productivity. The approach was selected for practical reasons as it permits application of a simple correction for soil structure and serves as a proof of concept for evaluating the importance of this omitted soil attribute. Preliminary results of Fatichi et al. (2020) are depicted in Figure 2 and confirm a putative role for soil structure under certain conditions with respect to runoff generation, infiltration and drainage (leakage for shallow profiles) and the average water content in the soil profile. The results also highlight complex interactions between rainfall characteristics, vegetation cover, and soil type such that in certain locations soil structure plays only a limited role in modifying surface fluxes. For example, in sandy soils, soil structure plays a relatively minor role compared to the response in loamy and clayey soils. Additionally, intense precipitation accentuates effects of soil structure relative to low intensity (drizzle) rainfall. The more challenging and complex question of how inclusion of soil structure could affect global climate has been studied using a global atmospheric circulation model (Ocean‐Land‐Atmosphere Model; Walko & Avissar, 2008). Results are beyond the scope of this perspective; however, persistent signatures of soil structure effects emerge in certain regions and periods of the year across 15 years of global simulations (Fatichi et al. 2020).


Modeling effects of soil structure parameter inclusion on near‐surface fluxes for different biomes and climates (Simone Fatichi, ETH—unpublished ). (a and b) Mean water content profiles with and without soil structure considerations for two study sites with different climatic and vegetation conditions; (c) effects on annual surface runoff for 20 locations studied (general decrease) and effects on mean annual leakage/drainage from soil profiles for 20 locations studied (exhibiting a general increase). Soil structure linked with vegetation traits (Gross Primary Production), results with original hydraulic properties (VG—black circles) and modified by soil structure (VG+SS—red triangles).

The criticism of present PTFs reflects, in part, unrealistic expectations from these products of correlations with a few and only partially representative soil attributes. We have shown above that the omission of soil structure could significantly modify surface hydrology beyond what soil texture information conveys. Regardless of the many limitations outlined above, PTFs are here to stay, and the community must find ways to improve their usefulness by leveraging additional information and application of PTFs more judiciously. One avenue for reducing effects of ambiguous parameterization is to seek simple and minimalistic model structures (Clark et al., 2017). This strategy aims to reduce self‐compensating parameter and model errors as discussed by Klemes (1983) and in the context of equifinality, by Beven (2001). Another option is to impose multiple physical constraints during SHP estimation to weed out unphysical parameter combinations as illustrated in a recent study by Lehmann et al. (2020). They explored an approach to improve PTF‐SHP estimation by requiring SHP to simultaneously fit measured soil water retention curve and satisfy a compatible soil evaporation characteristic length (L C ) using the same parameters (Lehmann et al., 2008).

Figure 3 illustrates how unconstrained values of the evaporation characteristic length (L C ) calculated from the van Genuchten parameters α and n for a popular database Rosetta (Schaap et al., 2001) are distributed, relative theoretically calculated values of L C for each soil textural class represented by the parameter n (red line). L C based on mean parameter values from the Unsaturated Soil Hydraulic Database (UNSODA) database (Nemes et al., 2001) is also shown. The cloud of data points exceeding the theoretical values in Figure 3a is attributed to “unphysical” parameter combinations (α and n ) in the global database (Lehmann et al., 2020). It is argued that theoretical L C values must remain within a physical range that marks the limiting depth (length) of capillary continuity with an evaporating soil surface during stage 1 evaporation (details in Lehmann et al., 2008). It is interesting to note that the subset of data shown in Figure 3b represents parameters for African desert soils where the unphysical deviations are less pronounced. This could reflect the lack of soil structure that tend to accentuate unphysical parameter combinations (as seen in Figure 3a with high L C values) especially for clay loam soils with 1.4 > n > 1.2. The conformity of African desert soil may also be related to the limited number and distribution of soil samples from these desert regions. Figure 4 illustrates how constraints for SHP estimation remove spurious values of L C while retaining good fit to retention data. The resulting “constrained” parameters α and n for the entire UNSODA database are clearly different as seen in Figures 4c and 4d. The consequences of these new SHP on model performance have not yet been rigorously tested; hence, this serves as an illustration and a proof of concept for constraining PTF‐SHP estimation.

(a) The distribution of calculated soil evaporation characteristic lengths LC based on parameters from the Rosetta database with unrealistic values for 1.6 > n > 1.2 (corresponding to loam or clay loam soil); (b) The distribution of LC based on Rosetta and mean values form UNSODA for African desert soils. The theoretical value of LC for the soil texture (represented by VG n parameter) described by the red line. Note soil texture distributions in inset of Figure 3a (Peter Lehmann, ETH—unpublished).

Constraining the estimation of van Genuchten α and n parameters by simultaneously fitting the (a) soil water retention curve data (an example) and an (b) evaporation characteristic length LC (red, constrained, and blue, unconstrained). The resulting changes in values of (c) the n parameter and (d) α parameter (parameters for the example in (a) marked by large symbols). Constrained fit had only minor effects on the quality of fit to water retention data (Peter Lehmann, ETH—unpublished).

It is useful to provide some context for the practice of using large‐scale and long‐term hydrologic system response to optimize and tune SHP (Gutmann & Small, 2007; de Lannoy et al., 2014). While such approaches are useful for diagnosing and identifying limitations of models and parameters, the tuning without systematic and physically based frameworks may hinder future updates of soil and PTF information and contribute to persistence of empirical elements. Modern observations offer new capabilities for evaluating model performance and thus could be harnessed to systematically improve PTF‐SHP estimation schemes anchored in tractable, updatable and physically based frameworks.

1.5 Lessons of Going Global

Most of my past research has been devoted to solving small‐scale puzzles (pores to samples). In recent years, however, our group and others in the soil‐hydrology community learned to embrace the challenge of extending small‐scale physics to global scale phenomena. For example, via the application of soil‐based surface evaporation resistance toward reducing empiricism in global soil evaporation models (Lehmann et al., 2018; Or & Lehmann, 2019). Growing awareness of the importance of large‐scale processes and the recognition of potential synergies among small and large scales have been promoted with closer interactions among global‐scale climate and ecological modelers. For example, interactions facilitated via the International Soil Modeling Consortium launched in 2016 (Vereecken et al., 2016; https://soil‐ and the GEWEX‐SoilWat initiative that brought together soil, hydrology, and climate people. I recall that a better part of the first day of a GEWEX‐SoilWat planning workshop in Leipzig (June, 2016) was devoted to a lively debate regarding what should the minimal spatial scale of process representation be. Soil physicists were adamant that a spatial representation exceeding several meters is meaningless, whereas climate modelers repeatedly insisted that anything less than a few kilometers is not feasible for global scale climate processes. A compromise of 1‐km scale finally paved the way for more productive discussions. As we engage in the journey of taking soil processes to global scales, we appreciate the value of pragmatism and the need to set aside the quest for universal solutions in favor of small steps; we also rediscover the importance of interdisciplinary exchange and learning the language that form the basis for productive compromises made at various scales. It also allows us to reflect on the challenges of “small scales” and their place in contemporary hydrology. Despite a certain level of dissatisfaction with conceptual shortcomings, the hydrology community is maturing and employs sophisticated methods and frameworks. We are learning to deal with and embrace the challenges (and opportunities) presented by big data, to handle phenomena at multiple scales and to systematically evaluate models and estimate parameters. The hydrology community have made considerable progress in addressing some challenges considered insurmountable only a few years ago:

  • Taming equifinality (or nonuniqueness)
  • – Studies have expanded the requirements for estimation of consistent sets of parameters by applying physically based constraints that reduce unwarranted degrees of freedom. The need for ad hoc parameter tuning is being reduced where possible by replacing empirical coefficients with physically based and paving the way for future updates as information becomes available, assembling simple and testable models and harnessing data availability at all scales to improve system representation.
  • Applying the test of time to models
  • – It is now the rule rather than the exception to use model “predictions” over extended periods under different conditions to improve parameter and model tuning. Progress in this respect reflects the increase in data availability and the prominence of “climatic” perspectives that are built on long‐term observations and averaging.
  • Capitalizing on large‐scale emergent behavior
  • – What was once a challenge of explaining and predicting the intrinsic nonlinearities of emergent system‐scale behavior, is now “turned on its head” and used for evaluation of model predictions (i.e., large‐scale runoff models used to test evaporation estimates). The Budyko (1963) framework has been used to study hydrologic response to changing climate at a continental scale (Donohue et al., 2012). The Bouchet (1963) complementary relations used in studies by Morton (1978) is another example of an emergent large‐scale phenomenon that could constrain predictions of evaporation and water balance of large regions (Zhang et al., 2010). The application of such large‐scale emergent behaviors has not yet been integrated to provide routine milestones for model evaluation (primarily due to incompatibility with spatial and temporal scales of gridded GCM, Earth System Models, and hydrological distributed models). Nevertheless, more and more studies report successful applications of these concepts for model evaluation often in the hydroclimatic context.
  • The tremendous scientific and technological progress of the past few decades places hydrology on the right track. Clearly, we are “not there yet” and the small‐scale challenges will remain unresolved in the foreseeable future. We have learned much from the small‐scale debate and from the thought‐provoking criticism of Klemes (1986), yet the question of “Dilettantism in hydrology: Transition or destiny?” has been settled; hydrology was never destined to amateurism (Burges, 2011).


    I gratefully acknowledge the nomination by John Selker and the trust and support of Andy Binley, Efi Foufoula‐Georgiou, and Harry Vereecken and the great honor bestowed by the Hydrology section of the AGU. I am grateful for the stimulating scientific collaborations in our research group at ETH with the contributions of Peter Lehmann, Sara Bonetti, Samuel Bickel, Surya Gupta, and Andreas Papritz. The interactions with Simone Fatichi (ETH), Bob Walko (U. Miami), and members of the NSF‐PIRE proposal “Soil goes global.” The study benefited from the many insights learned in the SoilWat‐GEWEX initiative (Sonia Seneviratne and others), the leadership of Harry Vereecken and Michael Young with the International Soil Modeling Consortium, and insightful discussions with Tissa Illangasekare and Casey Miller on our long car trip from the GRC in Maine. Finally, I thank with great appreciation and love my wife Angela for her love and support. I thank Siva Sivapalan, Luis Samaniego, and an anonymous reviewer for their insightful comments that helped improve the quality of the manuscript. A previous version of this manuscript was published in the Hydrology Section newsletter (December 2018).

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