Here, we review in depth how soils can remember moisture anomalies across spatial and temporal scales, embedded in the concept of soil moisture memory (SMM), and we explain the mechanisms and factors that initiate and control SMM. Specifically, we explore external and internal drivers that affect SMM, including extremes, atmospheric variables, anthropogenic activities, soil and vegetation properties, soil hydrologic processes, and groundwater dynamics. We analyze how SMM considerations should affect sampling frequency and data source collection. We discuss the impact of SMM on weather variability, land surface energy balance, extreme events (drought, wildfire, and flood), water use efficiency, and biogeochemical cycles. We also discuss the effects of SMM on various land surface processes, focusing on the coupling between soil moisture, water and energy balance, vegetation dynamics, and feedback on the atmosphere. We address the spatiotemporal variability of SMM and how it is affected by seasonal variation, location, and soil depth. Regarding the representation and integration of SMM in land surface models, we provide insights on how to improve predictions and parameterizations in LSMs and address model complexity issues. The possible use of satellite observations for identifying and quantifying SMM is also explored, emphasizing the need for greater temporal frequency, spatial resolution, and coverage of measurements. We provide guidance for further research and practical applications by providing a comprehensive definition of SMM, considering its multifaceted perspective.

Estimating of soil sorptivity ( S ) and saturated hydraulic conductivity ( K s ) parameters by field infiltration tests are widespread due to the ease of the experimental protocol and data treatment. The analytical equation proposed by Haverkamp et al. (1994) allows the modeling of the cumulative infiltration process, from which the hydraulic parameters can be estimated. This model depends on both initial and final values of the soil hydraulic conductivity, initial soil sorptivity, the volumetric water content increase ( ∆ θ ), and two infiltration constants, the so-called β and γ parameters. However, to reduce the number of unknown variables when inverting experimental data, constant parameters such as β and γ are usually prefixed to 0.6 and 0.75, respectively. In this study, the values of these constants are investigated using numerical infiltration curves for different soil types and initial soil water contents for the van Genuchten-Mualem (vGM) soil hydraulic model. Our approach considers the long-time expansions of the Haverkamp model, the exact soil properties such as S , K s , and initial soil moisture to derive the value of the β and γ parameters for each specific case. We then generated numerically cumulative infiltration curves using Hydrus 3-D software and fitted the long-time expansions to derive the value of the β and γ parameters. The results show that these parameters are influenced by the initial soil water content and the soil type. However, for initially dry soil conditions, some prefixed values can be proposed instead of the currently used values. If an accurate estimate of S and K s is the case, then for coarse-textured soils such as sand and loamy sand, we propose the use of 0.9 for both constants. For the remaining soils, the value of 0.75 can be retained for γ . For β constant, 0.75 and 1.5 values can be considered for, intermediate permeable soils (sandy loam and loam) and low permeable soils (silty loam and silt), respectively. We clarify that the results are based on using the vGM model to describe the hydraulic functions of the soil and that the results may differ, and the assumptions may change for other models.

Modelling of the land surface water-, energy-, and carbon balance provides insight into the behaviour of the Earth System, under current and future conditions. Currently, there exists a substantial variability between model outputs, for a range of model types, whereby differences between model input parameters could be an important reason. For large-scale land surface, hydrological, and crop models, soil hydraulic properties (SHP) are required as inputs, which are estimated from pedotransfer functions (PTFs). To analyse the functional sensitivity of widely used PTFs, the water fluxes for different scenarios using HYDRUS-1D was simulated and predictions compared. The results showed that using different PTFs causes substantial variability in predicted fluxes. In addition, an in-depth analysis of the soil SHPs and derived soil characteristics was performed to analyse why the SHPs estimated from the different PTFs cause the model to behave differently. The results obtained provide guidelines for the selection of PTFs in large scale models. The model performance in terms of numerical stability, time-integrated behaviour of cumulative fluxes, as well as instantaneous fluxes was evaluated, in order to compare the suitability of the PTFs. Based on this, the Rosetta, Wösten, and Tóth PTF seem to be the most robust PTFs for the Mualem van Genuchten SHPs and the PTF of Cosby et al. (1984) for the Brooks Corey functions. Based on our findings, we strongly recommend to harmonize the PTFs used in model inter-comparison studies to avoid artefacts originating from the choice of PTF rather from different model structures.

In his seminal paper on solution of the infiltration equation, Philip (1957) proposed a gravity time, tgrav, to estimate practical convergence time of his infinite time series expansion, TSE. The parameter tgrav refers to a point in time where infiltration is dominated equally by capillarity and gravity derived from the first two (dominant) terms of the TSE expansion. Evidence that higher order TSE terms describe the infiltration process better for longer times. Since the conceptual definition of tgrav is valid regardless of the infiltration model used, we opted to reformulate tgrav using the analytic approximation proposed by Parlange et al. (1982) valid for all times. In addition to the roles of soil sorptivity (S) and saturated (Ks) and initial (Ki) hydraulic conductivities, we explored effects of a soil specific shape parameter β on the behavior of tgrav. We show that the reformulated tgrav (notably tgrav= F(β) S^2/(Ks - Ki)^2 where F(β) is a β-dependent function) is about 3 times larger than the classical tgrav given by tgrav, Philip= S^2/(Ks - Ki)^2. The differences between original tgrav, Philip and the revised tgrav increase for fine textured soils. Results show that the proposed tgrav is a better indicator for convergence time than tgrav, Philip. For attainment of the steady-state infiltration, both time parameters are suitable for coarse-textured soils, but not for fine-textured soils for which tgrav is too conservative and tgrav, Philip too short. Using tgrav will improve predictions of the soil hydraulic parameters (particularly Ks) from infiltration data as compared to tgrav, Philip.