ANALYSIS OF THE SOIL MOISTURE BEHAVIOUR DURING WETTING AND DRYING EPISODES FROM TDR DATA COLLECTED AT PALLANZENO (TOCE VALLEY)

http://www.map.meteoswiss.ch/map-doc/NL15/menziani.pd

General analytical solutions of the linearized Richards equation for a half-space and a limited-layer domains

This paper aims to describe a compilation of solutions of the linearized one-dimensional Richards equation, solved both in a half-space and in a limited-layer domain. The solution, that is the soil water content at any required time and depth, is the sum of two components, one related to the initial condition and to null boundary conditions and the other related to the boundary conditions and to a null initial condition. The sum of the two quoted components is the general solution of the Richards equation in integral form; the analytical expression of the soil water content distribution is therefore obtained if the integrals in the solution can be solved. Besides the integral form solution, another solution holding for any initial and boundary conditions represented with step functions is described in the paper. The initial condition is always the soil water content profile (e.g. the one experimentally measured) while the boundary conditions are different for the two domains. For the half-space domain, the boundary condition can be the soil water content at the surface or the surface flux (e.g. the measured precipitation or evaporation). For this domain, the solution, with the supplementary conditions expressed as step functions, is obtained using a procedure, which accounts for the effects of the hydrological conditions of the soil on the flux at the surface. Therefore, this procedure is able to switch between successive atmosphere-controlled and soil-controlled phases of infiltration or evaporation, as required by the given boundary condition. The procedure provides the ponding time, the desiccation time and the surface water flux during the soil-controlled phases. For the limited-layer domain, the top and bottom boundary conditions are given as time dependent soil water content trends. Also for the limited-layer, a solution, obtained approximating the supplementary conditions with step functions, is derived using the basic solution, which is here presented. It provides the soil water content profile evolution, the top and bottom instantaneous and cumulative fluxes and the water gained by the soil layer in a specified time interval. Lastly, a comparison between the procedure results and an exact analytical solution is discussed

EVOLUZIONE DEL CONTENUTO VOLUMETRICO D\u2019ACQUA IN UNO STRATO FINITO OMOGENEO: SOLUZIONI ANALITICHE E MISURE SPERIMENTALI

Vengono presentate soluzioni dell\u2019equazione di Richards linearizzata e unidimensionale, con condizioni supplementari arbitrarie. Queste soluzioni forniscono l\u2019evoluzione temporale del contenuto volumetrico d\u2019acqua in ogni punto di un mezzo poroso non saturo, approssimabile con uno strato omogeneo di profondit\ue0 finita.La condizione iniziale pu\uf2 essere un qualsiasi profilo di contenuto volumetrico d\u2019acqua misurato sperimentalmente e quindi costituito da dati discreti. Parimenti, l\u2019evoluzione temporale del contenuto volumetrico d\u2019acqua, misurata a due profondit\ue0 ad intervalli temporali discreti, pu\uf2 rappresentare le condizioni ai bordi.Il profilo del contenuto volumetrico d\u2019acqua \ue8 misurato in due stazioni, installate nella conoide gigante del fiume Taro, non lontano dalla citt\ue0 di Parma. Le misure sono iniziate nell\u2019estate del 2006. Presso una delle stazioni sono in funzione anche alcuni sensori meteorologici (temperatura ed umidit\ue0 dell\u2019aria a due altezze, pressione, precipitazione). Recentemente, la stazione meteorologica \ue8 stata completata con le misure di velocit\ue0 e direzione del vento, radiazione solare netta e flusso di calore nel suolo. In questo modo sar\ue0 possibile stimare l\u2019evaporazione e quindi avere una misura del flusso in uscita attraverso l\u2019interfaccia aria-suolo, oltre a quello in entrata (precipitazione). Gli andamenti temporali del contenuto volumetrico d\u2019acqua mostrano una dipendenza dalla profondit\ue0: le sonde pi\uf9 superficiali presentano un\u2019elevata variabilit\ue0 mentre le pi\uf9 profonde hanno andamento smussato e lentamente variabile. Verranno presentati confronti tra le soluzioni analitiche dell\u2019equazione di Richards, con la schematizzazione descritta, ed i dati sperimentali, per brevi periodi temporali durante i quali \ue8 stato misurato un andamento lineare del contenuto volumetrico d\u2019acqua pi\uf9 superficiale

Analytical solutions of the linearized Richards equationwith flux boundary conditions for a half space and afinite layer

A useful insight of physical mechanisms related to the complex hydrological problems can be provided by analytical solutions of differential flow equations (e.g. Richards equation). Although analytical solutions may be not suitable to solve complex hydrological problems, they are fast and useful to test numerical procedures. The aim of this work is the study of the water flow in a sub-surface unsaturated layer (Vadose zone).In this context, the linearized Richards equation is analytically solved for arbitrary flux boundary conditions and arbitrary soil moisture initial conditions. Approximating the supplementary conditions by step-wise functions, the solution results a sumof solutions obtained for constant boundary conditions. This approach is quite useful because it permits to use standard meteorological data as boundary conditions. In fact, it can be used precipitation data as incoming flux and evaporation from Bowen ratio data as outgoing flux; these data are very common, while soil volumetric water content measurements are usually not available exactly at the soil-atmosphere interface. The study is extended to a finite layer schematisation, which can represent a real situation, in case of a shallow water table. The aforementioned solutions hold till the saturation is reached; after saturation behaviour is under study

HYDROMETEOROLOGICAL MEASUREMENTS IN THE TARO RIVER GIANT ALLUVIAL FAN

In the framework of the National Project: “Esplorazione geofisica e geologica di alcuni complessi acquiferi alluvionali nella pianura Padana tra Milano e Bologna, per la modellazione della circolazione idrica sotterranea”, the soil water content profile in the surface soil is measured at two stations located between the town of Parma and the Taro River (Po valley). The physical structure of the Taro River giant alluvial fan is well known because of the previous studies of the University of Parma geologists involved in the same National Project. On the basis of this knowledge, one station was installed at the site of the well #1 of Roncopascolo and the other at a site closer to the Taro River (Barilla field). At Roncopascolo, meteorological data are also collected, including air temperature and relative humidity at two levels, while, at Barilla field, only the soil moisture profile is measured. The aim is to study the partition of the water entering the surface of the soil in: evaporation, run off, water stored in the measured soil column and percolation towards the deeper layers. The soil water content measurements are performed with Frequency Domain Reflectometry (FDR) sensors; the scaled frequencies and the meteorological data are automatically collected and stored in a data logger and then transmitted when required. Roncopascolo station started at the end of July 2006, while Barilla station started in October 2006. At both stations, soil samples were taken for the laboratory determination of the soil physical characteristics. The time variation of the water stored in the studied soil columns is estimated by means of the mass balance method. From the data collected in the summer period, the evaporation is estimated. Similarly, applying the mass balance method to the data collected during and after heavy precipitation events, the water infiltrated into the soil can be estimated. Furthermore, the time evolution of the soil moisture profile is studied solving the linearized one-dimensional Richards equation for discrete arbitrary initial and boundary conditions. The results are the soil water content at any required time and depth in a semi-infinite unsaturated porous medium domain, the ponding time, the desiccation time and the surface water flux during the soil-controlled phases of infiltration or evaporation

General analytical solutions of the linearized Richards equation for a half-space and a finite-thickness domain

This paper aims to describe a compilation of solutions of the linearized one-dimensional Richards equation, solved both in a half-space and in a finite-thickness domain. The solution (the soil water content at any time and depth) can be represented as the sum of two components, one related to the initial condition and to null boundary conditions and the other related to the boundary conditions and to a null initial condition. The sum of the two quoted components is the general solution of the Richards equation in integral form; the analytical expression of the soil water content distribution is therefore obtained if the integrals in the solution can be solved. Besides the integral form solution, another solution holding for any initial and boundary conditions represented with step functions is described in the paper. The initial condition is always the soil water content profile (e.g. the one experimentally measured) while the boundary conditions are different for the two domains. For the half-space domain, the boundary condition can be the soil water content at the surface or the surface flux (e.g. the measured precipitation or evaporation). For this domain, the solution, with the initial-boundary conditions expressed as step functions, is obtained using a procedure, which accounts for the effects of the hydrological conditions of the soil on the flux at the surface. Therefore, this procedure is able to switch between successive atmosphere-controlled and soil-controlled phases of infiltration or evaporation, as required by the given boundary condition. The procedure provides the ponding time, the desiccation time and the surface water flux during the soil-controlled phases. For the finite-thickness domain, the top and bottom boundary conditions are given as time dependent soil water content trends. Also for the finite-thickness domain, a solution, obtained approximating the initial-boundary conditions with step functions, is derived using the basic solution. It provides the soil water content profile evolution, the top and bottom instantaneous and cumulative fluxes and the water gained by the soil layer in a specified time interval. Lastly, a comparison between the procedure results and an exact analytical solution is discussed

TIME SERIES OF SOIL WATER CONTENT MEASUREMENTS IN THE TARO RIVER GIANT ALLUVIAL FAN

The soil water content profile in the surface soil has been measured at two stations located between the town of Parma and the Taro River (Po valley) for few years. At one of the two stations, some meteorological data are also collected, including air temperature and relative humidity at two levels besides atmospheric pressure and precipitation. The soil water content measurements are performed with Frequency Domain Reflectometry (FDR) sensors; the scaled frequencies and the meteorological data are automatically collected and stored in a data logger and then transmitted when required. The aim is to study the partition of the water entering the surface of the soil in: evaporation, run off, water stored in the measured soil column and percolation towards the deeper layers. The readings show a clear dependence on the soil depth; a high variability characterizes the superficial probes while the deeper ones show smoother trends. Due to the reduced precipitation during 2008 summer-autumn seasons, the soil water content at 1.5 m reached the maximum value measured the previous year only about at the middle of January. Vice versa, the soil water content at 2 m depth never reached the previous winter value; it had its maximum in February. During some drying periods, a linear trend of the soil water content well represents the measurements collected at the shallowest levels. These data also show a daily oscillation damping with the depth. A new hydrological station is going to be installed very close to the Taro River. Moreover, the meteorological station, located in the Enia area of the well #1 of Roncopascolo, is now completed with new sensors, which permit to compute all the terms of the energy balance equation required to estimate the evaporation into the atmosphere

Situazioni di scambio del controllo sui processi di infiltrazione ed evaporazione dall’ atmosfera al suolo e viceversa

Vengono presentate soluzioni dell’equazione unidimensionale di Richards linearizzata, con condizioni iniziali e al bordo arbitrarie. Queste soluzioni forniscono l’evoluzione temporale del contenuto d’acqua in ogni punto di un mezzo poroso non saturo approssimabile con un semispazio.La condizione iniziale può essere un qualsiasi profilo di contenuto volumetrico d’acqua misurato sperimentalmente e quindi costituito da dati discreti. La condizione al bordo superiore può essere un qualsiasi flusso (discreto) applicato alla superficie, per esempio la precipitazione misurata sperimentalmente da un pluviometro di una stazione meteorologica.Con la procedura messa a punto è possibile seguire l’evoluzione del contenuto volumetrico d’acqua nel mezzo poroso durante periodi successivi di evaporazione ed infiltrazione controllati sia dall’atmosfera che dal suolo. Quando un suolo, inizialmente non saturo, viene sottoposto ad un flusso in ingresso maggiore della capacità del terreno di assorbire acqua, dopo un certo tempo, alla superficie, viene raggiunta la saturazione e l’acqua inizia a ristagnare (ponding, runoff). Viceversa, quando un suolo, inizialmente umido, viene sottoposto dalla richiesta atmosferica ad una certa evaporazione, se il processo dura abbastanza a lungo, può essere raggiunto, alla superficie, un valore di umidità del terreno così basso (valore a cui il terreno è secco come l’atmosfera sovrastante) che il flusso in uscita scende al di sotto della richiesta dell’atmosfera. In questi casi la procedura fornisce il tempo in cui, alla superficie, è raggiunta la saturazione o il valore minimo dell’umidità e fornisce, inoltre, il valore del flusso.La sinergia idro-meteorologica è evidente. Le misure meteorologiche locali (precipitazioni, gradienti di umidità e temperatura dell’aria, etc.) possono fornire il flusso all’interfaccia aria-suolo quando questo è controllato dall’atmosfera. Viceversa, il flusso può essere fornito dalla procedura ai modelli meteorologici, quando è controllato dal suolo

Analytical solutions of the linearized Richards equation for discrete arbitrary initial and boundary conditions

Solutions of the linearized one-dimensional Richards equation for discrete arbitrary initial and boundary conditions are presented. The result is the soil water content at any required time and depth in a semi-infinite unsaturated porous medium domain. The initial condition can be any discrete soil water content profile (e.g., experimentally measured) and the boundary condition can be any discrete water flux applied at the surface (e.g., experimentally derived). The procedure described in the paper is valid for any series of successive atmosphere-controlled and soil-controlled phases of infiltration or evaporation as required by the given boundary condition. The procedure provides the ponding time, the desiccation time and the surface water flux during the soil-controlled phases. The comparison among the proposed solutions and some exact analytical solutions is presented as well as the cumulative fluxes. As expected, the agreement between the proposed solutions and the exact analytical solutions depend on the time step chosen for the boundary condition and on the space step chosen for the initial condition. (c) 2006 Elsevier B.V.. All rights reserved

MICROELEMENTI NELLE ACQUE NATURALI DELLA PIANURA PADANA CON FLUORESCENZA X INDOTTA DA PROTONI ACCELERATI

Vengono presentati valori di concentrazione detreminati con la tecnica PIXE in acque sotterranee della pianura padana