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Fabio Castelli and Ignacio Rodriguez-Iturbe

Abstract

Attention is focused on the dynamical coupling between the soil moisture and atmospheric processes, such as in the presence of a growing moist baroclinic wave. A simplified scheme, representing the mass and energy exchanges between the soil and the atmospheric boundary layer, is incorporated into the inviscid semigeostrophic equations for the evolution of a meridionally independent baroclinic disturbance in the moist atmosphere. The model is formulated in terms of coupled, nonlinear, ordinary differential equations, allowing for simple and extensive numerical simulation. Using such an approach, the question is addressed to what extent and through which mechanisms a heterogeneous soil moisture distribution affects the evolution of the baroclinic waves and in particular the estimate of the potential precipitation. The interaction between land and atmosphere is found to have both a local effect and a large-scale effect. The local effect consists of modifying the vertical lapse rates of dry and equivalent potential temperatures in the troposphere. The large-scale effect is realized through the global dynamics of the baroclinic wave and in particular through the rates of mass and energy advection and the strength of the ageostrophic frontal circulation, which depend strongly themselves on the temperature lapse rates. Both mechanisms are found to be substantially dependent on both the local moisture content of the soil and on the large-scale moisture differences, highlighting their feedback on precipitation.

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Edoardo Daly, Amilcare Porporato, and Ignacio Rodriguez-Iturbe

Abstract

The governing equations of soil moisture dynamics, photosynthesis, and transpiration are reviewed and coupled to study the dependence of plant carbon assimilation on soil moisture. The model follows the scheme of the soil–plant–atmosphere continuum (SPAC) and uses a simplified model of the atmospheric boundary layer to arrive at an upscaled, parsimonious representation at the daily time scale. The analysis of soil moisture, transpiration, and carbon assimilation dynamics provides an assessment of the role of soil, plant, and boundary layer characteristics on the diurnal courses of photosynthesis and transpiration rates, while the subsequent upscaling at the daily level provides a functional dependence of stomatal conductance on soil moisture that is in good agreement with field experiments. The upscaled dependence of transpiration and carbon assimilation on soil moisture is used in of this paper to explore the impact of soil moisture dynamics on plant conditions when rainfall variability is explicitly considered.

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Edoardo Daly, Amilcare Porporato, and Ignacio Rodriguez-Iturbe

Abstract

The coupled dynamics of soil moisture, transpiration, and assimilation are studied at the daily time scale by temporally upscaling the hourly time scale results obtained in a companion paper. The effects of soil and vegetation characteristics on soil moisture dynamics at the daily time scale and the parameters characterizing the dependence of transpiration and assimilation on soil water content are analyzed and discussed. The daily leaf carbon assimilation is then coupled to a stochastic soil moisture model to obtain a probabilistic description of the carbon assimilation during a growing season. The rainfall regime, in terms of both frequency and amount of precipitation, controls the mean assimilation during a growing season that reaches a maximum for an intermediate range of daily rainfall probabilities, indicating the existence of a rainfall regime that is most effective for plant productivity. The analysis of the duration and frequency of periods of no assimilation provides a measure of plant water stress as a function of the soil, vegetation, and climate characteristics. The results are in good agreement with the dynamic water stress defined in Porporato et al. on the basis of the crossing properties of the stochastic soil moisture dynamics.

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Shafiqul Islam, Rafael L. Bras, and Ignacio Rodriguez-Iturbe

Abstract

There have been numerous attempts to detect the presence of deterministic chaos by estimating the correlation dimension. The values of reported correlation dimension for various geophysical time series vary between 1.3 and virtually infinity (i.e., no saturation). It is pointed out that analyzing variables that depend on physical constraints and thresholds, like precipitation, may lead to underestimation of the correlation dimension of the underlying dynamical system.

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Dara Entekhabi, Ignacio Rodriguez-Iturbe, and Rafael L. Bras

Abstract

Persistent and prolonged periods of dry or moist conditions are often evident in the interannual variability of continental-type climates This variability appears as fluctuations around several distinct and preferred moisture states. These fluctuations and transitions between the preferred states are commonly attributed to large-scale changes in atmospheric circulation patterns possibly caused by oceanic influence.

This paper argues that a major contributing factor to the persistent dry or moist behavior could be due to feedback and nonlinear interaction between the components of the hydrologic cycle in both the land and the atmosphere. A model that couples the water balance of continental landmasses and the overlying atmosphere is presented. The large-scale variabilities in atmospheric circulation are introduced by way of simple randomness in key forcing parameters. The result is a multiplicative-noise stochastic differential equation for the water balance dynamics of continental-type climates that includes land surface-atmosphere interaction.

The solution to this differential equation exhibits a bimodal probability distribution function for soil moisture and precipitation. Extended periods of anomalous dry conditions (drought) or alternatively wet conditions (pluvial), with abrupt transitions between them, are present in the model. The statistics of persistent anomalous conditions are analyzed for two climatic classifications. The probability distribution function for transitions out of droughts are developed for the modeled climates.

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Amilcare Porporato, Paolo D’Odorico, Luca Ridolfi, and Ignacio Rodriguez-Iturbe

Abstract

A simple model is developed to investigate the role of spatial dynamics in the soil–atmosphere system. The model is constructed by considering the mass and energy balance equations for soil and atmosphere, closed with a two-dimensional, corrected quasigeostrophic approximation for large-scale atmospheric motions, and a suitable model for rainfall occurrence. The main result presented concerns the linear stability analyses of the homogenous equilibrium solutions for dry and wet climates. In the first case (desert) the system is stable and no spatial perturbation internal to the system can produce spatial heterogeneities. In the second case (wet climate) the dynamics can produce spatial instabilities of several scales, resulting in likely patterns of wet and dry zones. A key role in triggering this instability is played by the sensible heat flux to the atmosphere, which in turn is linked to soil moisture.

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