scholarly journals Ecohydrology in Mediterranean areas: a numerical model to describe growing seasons out of phase with precipitations

2008 ◽  
Vol 12 (1) ◽  
pp. 303-316 ◽  
Author(s):  
D. Pumo ◽  
F. Viola ◽  
L. V. Noto
Keyword(s):  
Soil Moisture ◽  
Steady State ◽  
Water Stress ◽  
Numerical Model ◽  
Probability Density Function ◽  
Probability Density ◽  
Mediterranean Climate ◽  
Growing Season ◽  
Time Profile ◽  
Moisture Dynamics

Abstract. The probabilistic description of soil moisture dynamics is a relatively new topic in hydrology. The most common ecohydrological models start from a stochastic differential equation describing the soil water balance, where the unknown quantity, the soil moisture, depends both on spaces and time. Most of the solutions existing in literature are obtained in a probabilistic framework and under steady-state condition; even if this last condition allows the analytical handling of the problem, it has considerably simplified the same problem by subtracting generalities from it. The steady-state hypothesis, appears perfectly applicable in arid and semiarid climatic areas like those of African's or middle American's savannas, but it seems to be no more valid in areas with Mediterranean climate, where, notoriously, the wet season foregoes the growing season, recharging water into the soil. This moisture stored at the beginning of the growing season (known as soil moisture initial condition) has a great importance, especially for deep-rooted vegetation, by enabling survival in absence of rainfalls during the growing season and, however, keeping the water stress low during the first period of the same season. The aim of this paper is to analyze the soil moisture dynamics using a simple non-steady numerical ecohydrological model. The numerical model here proposed is able to reproduce soil moisture probability density function, obtained analytically in previous studies for different climates and soils in steady-state conditions; consequently it can be used to compute both the soil moisture time-profile and the vegetation static water stress time-profile in non-steady conditions. Here the differences between the steady-analytical and the non-steady numerical probability density functions are analyzed, showing how the proposed numerical model is able to capture the effects of winter recharge on the soil moisture. The dynamic water stress is also numerically evaluated, implicitly taking into account the soil moisture condition at the beginning of the growing season. It is also shown the role of different annual climatic parameterizations on the soil moisture probability density function and on the vegetation water stress evaluation. The proposed model is applied to a case study characteristic of Mediterranean climate: the watershed of Eleuterio in Sicily (Italy).

scholarly journals Ecohydrology in Mediterranean areas: a numerical model to describe growing seasons out of phase with precipitations

2007 ◽  
Vol 4 (5) ◽  
pp. 2769-2809
Author(s):  
D. Pumo ◽  
F. Viola ◽  
L. V. Noto
Keyword(s):  
Soil Moisture ◽  
Steady State ◽  
Water Stress ◽  
Numerical Model ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Growing Season ◽  
Time Profile ◽  
Moisture Dynamics

Abstract. The probabilistic description of soil moisture dynamics is a relatively new topic in hydrology. The most common ecohydrological models start from the soil water balance, a stochastic differential equation where the unknown quantity is the function of the soil moisture, depending both on spaces and time. Most of existing solutions in literature are obtained in a probabilistic framework and under steady-state condition; even if this last condition allows the analytical handling of the problem, it has considerably simplified the problem by subtracting generalities from it. The steady-state hypothesis, used in many ecohydrological works, appears perfectly applicable in arid and semiarid climatic areas like those of African's or middle American's savannas, but it seems to be no more valid in areas with Mediterranean climate, where, notoriously, the wet season foregoes the growing season, thus recharging the soil moisture. This initial condition, especially for deep rooted vegetation, has a great importance by enabling survival in absence of rainfalls during the growing season and, however, keeping the water stress low during its first period. The aim of this paper is to investigate the soil moisture dynamics using a simple non-steady numerical ecohydrological model. The numerical model is able to reproduce soil moisture probability density function, obtained analytically in previous studies for different climate and soil conditions in steady state conditions. The proposed model gives both the soil moisture time-profile and the vegetation static water stress time-profile. From the former it is possible to extract the probability density function of soil-moisture during the whole growing season, while the latter allows the estimation of the vegetation response to the water stress. Here the differences between the analytical and the numerical probability density functions are presented, showing how the numerical model is able to capture the effects of winter recharge on the soil moisture. The dynamic water stress is numerically evaluated, implicitly taking into account the soil moisture condition at the beginning of the growing season. The model proposed here is applied in the forested river basin of the Eleuterio in Sicily (Italy).

An improved energy envelope stochastic averaging method and its application to a nonlinear oscillator

2016 ◽  
Vol 23 (1) ◽  
pp. 119-130 ◽  
Author(s):  
Yaping Zhao
Keyword(s):  
Steady State ◽  
Probability Density Function ◽  
Probability Density ◽  
Averaging Method ◽  
Stochastic Averaging ◽  
Stochastic Averaging Method ◽  
System Response ◽  
Mean Square ◽  
Fpk Equation ◽  
The Mean

An improved stochastic averaging method of the energy envelope is proposed, whose application sphere is extensive and whose implementation is convenient. An oscillating system with both nonlinear damping and stiffness is taken into account. Its averaged Fokker-Planck-Kolmogorov (FPK) equation in respect of the transition probability density function of the energy envelope is deduced by virtue of the method mentioned above. Under the initial and boundary conditions, the joint probability density function as to the displacement and velocity of the system is worked out in closed form after solving the averaged FPK equation by right of a technique based on the integral transformation. With the aid of the special functions, the transient solutions of the probabilistic characteristics of the system response are further derived analytically, including the probability density functions and the mean square values. A simple approach to generate the ideal white noise is drastically ameliorated in order to produce the stationary wide-band stochastic external excitation for the Monte Carlo simulating investigation of the nonlinear system. Both the theoretical solution and the numerical solution of the probabilistic properties of the system response are obtained, which are extremely coincident with each other. The numerical simulation and the theoretical computation all show that the time factor has a certain influence on the probability characteristics of the response. For example, the probabilistic distribution of the displacement tends to be scattered and the mean square displacement trends toward its steady-state value as time goes by. Of course the transient process to reach the steady-state value will obviously be shorter if the damping of the system is greater.

scholarly journals Difference in Canopy and Air Temperature as an Indicator of Grassland Water Stress

2013 ◽  
Vol 1 (No. 4) ◽  
pp. 127-138 ◽  
Author(s):  
Duffková Renata
Keyword(s):  
Soil Moisture ◽  
Water Stress ◽  
Moisture Content ◽  
Air Temperature ◽  
Temperature Difference ◽  
Soil Moisture Content ◽  
Growing Season ◽  
Plant Residues ◽  
Dead Plant ◽  
Linear Correlations

In 2003–2005 in conditions of the moderately warm region of the Třeboň Basin (Czech Republic) the difference between canopy temperature (Tc) and air temperature at 2 m (Ta) was tested as an indicator of grass­land water stress. To evaluate water stress ten-minute averages of temperature difference Tc–Ta were chosen recorded on days without rainfall with intensive solar radiation from 11.00 to 14.00 CET. Water stress in the zone of the major portion of root biomass (0–0.2 m) in the peak growing season (minimum presence of dead plant residues) documented by a sudden increase in temperature difference, its value 5–12°C and unfavourable canopy temperatures due to overheating (> 30°C) was indicated after high values of suction pressure approach­ing the wilting point (1300 kPa) were reached. High variability of temperature difference in the conditions of sufficient supply of water to plants was explained by the amount of dead plant residues in canopy, value of va­pour pressure deficit (VPD), actual evapotranspiration rate (ETA) and soil moisture content. At the beginning of the growing season (presence of dead plant residues and voids) we proved moderately strong negative linear correlations of Tc–Ta with VPD and Tc–Ta with ETA rate and moderately strong positive linear correlations of ETA rate with VPD. In the period of intensive growth (the coverage of dead plant residues and voids lower than 10%) moderately strong linear correlations of Tc–Ta with VPD and multiple linear correlations of Tc–Ta with VPD and soil moisture content at a depth of 0.10–0.40 m were demonstrated.

scholarly journals Effect of Irrigation and Soil Water Stress on Densities of Macrophomina phaseolina in Soil and Roots of Two Soybean Cultivars

Plant Disease ◽  
2000 ◽  
Vol 84 (8) ◽  
pp. 895-900 ◽  
Author(s):  
S. R. Kendig ◽  
J. C. Rupe ◽  
H. D. Scott
Keyword(s):  
Soil Moisture ◽  
Water Stress ◽  
Soil Water ◽  
Growth Stage ◽  
Root Colonization ◽  
Growing Season ◽  
Moisture Stress ◽  
Macrophomina Phaseolina ◽  
Soil Moisture Stress ◽  
Soil Water Stress

The effects of irrigation and soil water stress on Macrophomina phaseolina microsclerotial (MS) densities in the soil and roots of soybean were studied in 1988, 1989, and 1990. Soybean cvs. Davis and Lloyd received irrigation until flowering (TAR2), after flowering (IAR2), full season (FSI), or not at all (NI). Soil water matric potentials at 15- and 30-cm depths were recorded throughout the growing season and used to schedule irrigation. Soil MS densities were determined at the beginning of each season. Root MS densities were determined periodically throughout the growing season. Microsclerotia were present in the roots of irrigated as well as nonirrigated soybean within 6 weeks after planting. By vegetative growth stage V13, these densities reached relatively stable levels in the NI and FSI treatments (2.23 to 2.35 and 1.35 to 1.63 log [microsclerotia per gram of dry root], respectively) through reproductive growth stage R6. After R6, irrigation was discontinued and root densities of microsclerotia increased in all treatments. Initiation (IAR2) or termination (TAR2) of irrigation at R2 resulted in significant changes in root MS densities, with densities reaching levels intermediate between those of FSI and NI treatments. Year to year differences in root colonization reflected differences in soil moisture due to rainfall. The rate of root colonization in response to soil moisture stress decreased with plant age. Root colonization was significantly greater in Davis than Lloyd at R5 and R8. This was reflected in a trend toward higher soil densities of M. phaseolina at planting in plots planted with Davis than in plots planted with Lloyd. Although no charcoal rot symptoms in the plant were observed in this study, these results indicated that water management can limit, but not prevent, colonization of soybean by M. phaseolina, that cultivars differ in colonization, and that these differences may affect soil densities of the fungus.

scholarly journals A Novel Limit Distribution for the Analysis of Randomly Mistuned Bladed Disks

1996 ◽  
Author(s):  
Marc P. Mignolet ◽  
Chung-Chih Lin
Keyword(s):  
Steady State ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Perturbation Technique ◽  
Practical Case ◽  
Numerical Examples ◽  
Critical Effect ◽  
Form Model ◽  
Steady State Amplitude

A recently introduced perturbation technique is employed to derive a novel closed form model for the probability density function of the resonant and near-resonant, steady state amplitude of blade response in randomly mistuned disks. In its most general form, this model is shown to involve six parameters but, in the important practical case of a pure stiffness (or frequency) mistuning, only three parameters are usually sufficient to completely specify this distribution. A series of numerical examples are presented that demonstrate the extreme reliability of this three-parameter model in accurately predicting the entire probability density function of the amplitude of response, and in particular the large amplitude tail of this distribution which is the most critical effect of mistuning.

A Novel Limit Distribution for the Analysis of Randomly Mistuned Bladed Disks1

2000 ◽  
Vol 123 (2) ◽  
pp. 388-394 ◽  
Author(s):  
M. P. Mignolet ◽  
C.-C. Lin ◽  
B. H. LaBorde
Keyword(s):  
Steady State ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Perturbation Technique ◽  
Practical Case ◽  
Numerical Examples ◽  
Critical Effect ◽  
Form Model ◽  
Steady State Amplitude

A recently introduced perturbation technique is employed to derive a novel closed form model for the probability density function of the resonant and near-resonant, steady state amplitude of blade response in randomly mistuned disks. In its most general form, this model is shown to involve six parameters but, in the important practical case of a pure stiffness (or frequency) mistuning, only three parameters are usually sufficient to completely specify this distribution. A series of numerical examples are presented that demonstrate the reliability of this three-parameter model in accurately predicting the entire probability density function of the amplitude of response, and in particular the large amplitude tail of this distribution, which is the most critical effect of mistuning.

scholarly journals The Impact of Land–Atmosphere Interactions on the Temporal Variability of Soil Moisture at the Regional Scale

2005 ◽  
Vol 6 (1) ◽  
pp. 53-67 ◽  
Author(s):  
John P. Kochendorfer ◽  
Jorge A. Ramírez
Keyword(s):  
Differential Equation ◽  
Soil Moisture ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Temporal Variability ◽  
Regional Scale ◽  
Precipitation Efficiency ◽  
Precipitation Recycling ◽  
The Impact

Abstract This study examines the impact of the nonlinear dynamics of soil-moisture feedbacks to precipitation on the temporal variability of soil moisture at the regional scale. It is a modeling study in which the large-scale soil-water balance is first formulated as an ordinary differential equation and then recast as a stochastic differential equation by incorporating colored noise representing the high-frequency temporal variability and correlation of precipitation. The underlying model couples the atmospheric and surface-water balances and accounts for both precipitation recycling and precipitation-efficiency feedbacks, which arise from the surface energy balance. Based on the governing Fokker–Planck equation, three different analytical solutions (corresponding to differing forms and combinations of feedbacks) are derived for the steady-state probability density function of soil moisture. Using NCEP–NCAR reanalysis data, estimates of potential evapotranspiration, and long-term observations of precipitation, streamflow, and soil moisture, the model is parameterized for a 5° × 5° region encompassing the state of Illinois. It is shown that precipitation-efficiency feedbacks can be significant contributors to the variability of soil moisture at the regional scale. Precipitation recycling, on the other hand, increases the variability by a negligible amount. For all feedback cases, the probability density function is unimodal and nearly symmetric. The analysis concludes with an examination of the dependence of the shape of the probability density functions on spatial scale. It is shown that the associated increases in either the correlation time scale or the variance of the noise will produce a bimodal distribution when precipitation-efficiency feedbacks are included. However, the magnitudes of the necessary increases are of an unrealistic magnitude.

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