Soil compaction and vegetation cover in a Scots pine stand at the Mediterranean rangelands

Right development of ROOT SYSTEMS is essential to ensure seedling survival in the initial stages of natural regeneration processes. Soil compaction determines this development both because of its influence on soil Tª & moisture dynamics and for its direct effect on soil mechanical impedance to root growth. All this effects can be assessed as a whole through soil penetration resistance (Soil Strength) measurements. SOIL STRENGTH has been usually evaluated in forest research in connection with severe disturbances derived from heavy machinery works during forest operations. Nevertheless, undisturbed soils are also expected to show different levels of compaction for root development. Organic matter modifies soil structure and so on porosity, compaction and resultant soil resistance to penetration. Its concentration in surface layers is rather related to vegetation cover composition and density. So within forest stands, a relationship is expected to be found between VEGETATION COVER density and compaction measured as resistance to penetration (soil strength)

Optimization of the irrigation time and irrigation frequency by using Hydrus-2D and a capacitance FDR sensor

The evolution of water content on a sandy soil during the sprinkler irrigation campaign, in the summer of 2010, of a field of sugar beet crop located at Valladolid (Spain) is assessed by a capacitive FDR (Frequency Domain Reflectometry) EnviroScan. This field is one of the experimental sites of the Spanish research center for the sugar beet development (AIMCRA). The objective of the work focus on monitoring the soil water content evolution of consecutive irrigations during the second two weeks of July (from the 12th to the 28th). These measurements will be used to simulate water movement by means of Hydrus-2D. The water probe logged water content readings (m3/m3) at 10, 20, 40 and 60 cm depth every 30 minutes. The probe was placed between two rows in one of the typical 12 x 15 m sprinkler irrigation framework. Furthermore, a texture analysis at the soil profile was also conducted. The irrigation frequency in this farm was set by the own personal farmer 0 s criteria that aiming to minimizing electricity pumping costs, used to irrigate at night and during the weekend i.e. longer irrigation frequency than expected. However, the high evapotranspiration rates and the weekly sugar beet water consumption—up to 50mm/week—clearly determined the need for lower this frequency. Moreover, farmer used to irrigate for six or five hours whilst results from the EnviroScan probe showed the soil profile reaching saturation point after the first three hours. It must be noted that AIMCRA provides to his members with a SMS service regarding weekly sugar beet water requirement; from the use of different meteorological stations and evapotranspiration pans, farmers have an idea of the weekly irrigation needs. Nevertheless, it is the farmer 0 s decision to decide how to irrigate. Thus, in order to minimize water stress and pumping costs, a suitable irrigation time and irrigation frequency was modeled with Hydrus-2D. Results for the period above mentioned showed values of water content ranging from 35 and 30 (m3/m3) for the first 10 and 20cm profile depth (two hours after irrigation) to the minimum 14 and 13 (m3/m3) ( two hours before irrigation). For the 40 and 60 cm profile depth, water content moves steadily across the dates: The greater the root activity the greater the water content variation. According to the results in the EnviroScan probe and the modeling in Hydrus-2D, shorter frequencies and irrigation times are suggested.

Short-term effects of four tillage practices on soil physical properties, soil water potential, and maize yield

The area cultivated using conservation tillage has recently increased in central Spain. However, soil compaction and water retention with conservation tillage still remains a genuine concern for landowners in this region be- cause of its potential effect on the crop growth and yield. The aim of this research is to determine the short- term influences of four tillage treatments on soil physical properties. In the experiment, bulk density, cone index, soil water potential, soil temperature and maize (Zea mays L.) productivity have been measured. A field experiment was established in spring of 2013 on a loamy soil. The experiment compared four tillage methods (zero tillage, ZT; reservoir tillage, RT; minimum tillage, MT; and conventional tillage, CT). Soil bulk density and soil cone index were measured during maize growing season and at harvesting time. Furthermore, the soil water potential was monitored by using a wireless sensors network with sensors at 20 and 40 cm depths. Also, soil temperatures were registered at depths of 5 and 12 cm. Results indicated that there were significant differ- ences between soil bulk density and cone index of ZT method and those of RT, MT, and CT, during the growing season; although, this difference was not significant at the time of harvesting in some soil layers. Overall, in most soil layers, tillage practice affected bulk density and cone index in the order: ZT N RT N MT N CT. Regardless oftheentireobservationperiod,results exhibited that soils under ZT and RT treatments usually resulted in higher water potential and lower soil temperature than the other two treatments at both soil depths. In addition, clear differences in maize grain yield were observed between ZT and CT treatments, with a grain yield (up to 15.4%) increase with the CT treatment. On the other hand, no significant differences among (RT, MT, and CT) on maizeyieldwerefound.Inconclusion,the impact of soil compaction increase and soil temperature decrease,pro- duced by ZT treatment is a potential reason for maize yield reduction in this tillage method. We found that RT could be certainly a viable option for farmers incentral Spain,particularly when switching to conservation tillage from conventional tillage. This technique showed a moderate and positive effect on soil physical properties and increased maize yields compared to ZT and MT, and provides an opportunity to stabilize maize yields compared to CT.

Effects of soil management in vineyard on soil physical and chemical characteristics

Cover crops in Mediterranean vineyards are scarcely used due to water competition between the cover crop and the grapevine; however, bare soil management through tillage or herbicides tends to have negative effects on the soil over time (organic matter decrease, soil structure and soil fertility degradation, compaction, etc). The objective of this study was to understand how soil management affects soil fertility, compaction and infiltration over time. To this end, two bare soil techniques were compared, tillage (TT) and total herbicide (HT) with two cover crops; annual cereal (CT) and annual grass (AGT), established for 8 years. CT treatment showed the highest organic matter content, having the biggest amount of biomass incorporated into the soil. The annual adventitious vegetation in TT treatment (568 kg dry matter ha-1) that was incorporated into the soil, kept the organic matter content higher than HT levels and close to AGT level, in spite of the greater aboveground annual biomass production of this treatment (3632 kg dry matter ha-1) whereas only its roots were incorporated into the soil. TT presented the highest bulk density under the tractor track lines and a greatest resistance to penetration (at 0.2 m depth). AGT presented bulk density values (upper 0.4 m) lower than TT and penetration resistance in CT lower (at 0.20 m depth) than TT too. Effects of soil management in vineyard on soil physical and chemical characteristics - ResearchGate. Available from: http://www.researchgate.net/publication/268520480_Effects_of_soil_management_in_vineyard_on_soil_physical_and_chemical_characteristics [accessed May 20, 2015].

Replacing bare fallow with cover crops in an irrigated cropping system: soil salinity and salt leaching

In irrigated areas where cover crop establishment can be assured, consequent soil or nutrient conservation could increase sustainability of cropping systems. Replacing bare fallow with cover crops may increase sustainability by enhancing soil aggregate stability, water retention capacity or controlling nitrate leaching. Nevertheless, adoption of cover crops increase evapotranspiration and reduce water percolation beyond the root systems; therefore, it could lead to salt accumulation in the upper soil layers. This study was conducted during four years to determine the effect of replacing bare fallow by a cover crop on soil salt accumulation and salt leaching in an irrigated maize production system.

The relationship between soil geochemistry and the bioaccessibility of trace elements in playground soil

A total of 32 samples of surficial soil were collected from 16 playground areas in Madrid (Spain), in order to investigate the importance of the geochemistry of the soil on subsequent bioaccessibility of trace elements. The in vitro bioaccessibility of As, Co, Cr, Cu, Ni, Pb and Zn was evaluated by means of two extraction processes that simulate the gastric environment and one that reproduces a gastric + intestinal digestion sequence. The results of the in vitro bioaccessibility were compared against aqua regia extractions (“total” concentration), and it was found that total concentrations of As, Cu, Pb and Zn were double those of bioaccessible values, whilst that of Cr was ten times higher. Whereas the results of the gastric + intestinal extraction were affected by a high uncertainty, both gastric methods offered very similar and consistent results, with bioaccessibilities following the order: As = Cu = Pb = Zn > Co > Ni > Cr, and ranging from 63 to 7 %. Selected soil properties including pH, organic matter, Fe and CaCO3 content were determined to assess their influence on trace element bioaccessibility, and it was found that Cu, Pb and Zn were predominantly bound to organic matter and, to a lesser extent, Fe oxides. The former fraction was readily accessible in the gastric solution, whereas Fe oxides seemed to recapture negatively charged chloride complexes of these elements in the gastric solution, lowering their bioaccessibility. The homogeneous pH of the playground soils included in the study does not influence trace element bioaccessibility to any significant extent except for Cr, where the very low gastric accessibility seems to be related to the strongly pH-dependent formation of complexes with organic matter. The results for As, which have been previously described and discussed in detail in Mingot et al. (Chemosphere 84: 1386–1391, 2011), indicate a high gastric bioaccessibility for this element as a consequence of its strong association with calcium carbonate and the ease with which these bonds are broken in the gastric solution. The calculation of risk assessments are therefore dependant on the methodology used and the specific environment they address. This has impacts on management strategies formulated to ensure that the most vulnerable of society, children, can live and play without adverse consequences to their health.

Forest Hydrology, Soil Conservation and Green Barriers in Canary Islands

In volcanic islands, the rainfall regime and its torrential nature, together with the steep slopes and the soil types present are considered to be some of the main factors affecting forest hydrology and soil conservation. In such environments, rain regime is generally irregular and characterized by short and intense rainfalls, which could cause destructive flows at times, followed by long periods of rain absence. The volcanic nature of these islands have as a direct resultant steep slopes which influences the runoff volume and speed, as well as the amount of topsoil susceptible to be detached and transported downstream. The soil type also affects the susceptibility to erosion processes. Andisols are the most typical soil on volcanic islands. Their particularities derive their mineral constituents, called short-range-order products, which provide these soils with an increased structural stability, which in turn reduces their susceptibility to erosion. However, the land use changes and the environmental factors such as rain regime and steep slopes may be determinant factor in destabilizing these soils and ultimately a cause for soil erosion and runoffs, which become a threat to the population downstream. Green barriers have been traditionally used to prevent or reduce these processes, also to enhance the dew effect and the fog water collection, and as a firebreak which acts as a barrier to slow or stop the progress of a wildfire. Wooded species present and subsequently their performance have a major influence on their effectiveness. The use of this natural erosion and fire control methods on volcanic islands is discussed in this paper.

The role of cover crops in irrigated systems: Soil salinity and salt leaching

Soil salinity and salt leaching are a risk for sustainable agricultural production in many irrigated areas. This study was conducted over 3.5 years to determine how replacing the usual winter fallow with a cover crop (CC) affects soil salt accumulation and salt leaching in irrigated systems. Treatments studied during the period between summer crops were: barley (Hordeum vulgare L.), vetch (Vicia villosa L.) and fallow. Soil water content was monitored daily to a depth of 1.3 m and used with the numerical model WAVE to calculate drainage. Electrical conductivity (EC) was measured in soil solutions periodically, and in the soil saturated paste extracts before sowing CC and maize. Salt leaching was calculated multiplying drainage by total dissolved salts in the soil solution, and use to obtain a salt balance. Total salt leaching over the four winter fallow periods was 26 Mg ha−1, whereas less than 18 Mg ha−1 in the presence of a CC. Periods of salt gain occurred more often in the CC than in the fallow. By the end of the experiment, net salt losses occurred in all treatments, owing to occasional periods of heavy rainfall. The CC were more prone than the fallow to reduce soil salt accumulation during the early growth stages of the subsequent cash crop.

Soil P and cation availability and crop uptake in a forage rotation under conventional and reduced tillage

Long-term conservation tillage can modify vertical distribution of nutrients in soil profiles and alter nutrient availability and yields of crops.

Determination of suitable irrigation lengths and intervals using capacitance humidity sensors for a sandy soil

production, during the summer of 2010. This farm is integrated at the Spanish research network for the sugar beet development (AIMCRA) which regarding irrigation, focuses on maximizing water saving and cost reduction. According to AIMCRA 0 s perspective for promoting irrigation best practices, it is essential to understand soil response to irrigation i.e. maximum irrigation length for each soil infiltration capacity. The Use of Humidity Sensors provides foundations to address soil 0 s behavior at the irrigation events and, therefore, to establish the boundaries regarding irrigation length and irrigation interval. In order to understand to what extent farmer 0 s performance at Tordesillas farm could have been potentially improved, this study aims to address suitable irrigation length and intervals for the given soil properties and evapotranspiration rates. In this sense, several humidity sensors were installed: (1) A Frequency Domain Reflectometry (FDR) EnviroScan Probe taking readings at 10, 20, 40 and 60cm depth and (2) different Time Domain Reflectometry (TDR) Echo 2 and Cr200 probes buried in a 50cm x 30cm x 50cm pit and placed along the walls at 10, 20, 30 and 40 cm depth. Moreover, in order to define soil properties, a textural analysis at the Tordesillas Farm was conducted. Also, data from the Tordesillas meteorological station was utilized.

Implementation of the Heated Pulsed Theory using actively heated fiber optics: measurements of soil volumetric water content and soil volumetric heat capacity

Existe una creciente necesidad de hacer el mejor uso del agua para regadío. Una alternativa eficiente consiste en la monitorización del contenido volumétrico de agua (θ), utilizando sensores de humedad. A pesar de existir una gran diversidad de sensores y tecnologías disponibles, actualmente ninguna de ellas permite obtener medidas distribuidas en perfiles verticales de un metro y en escalas laterales de 0.1-1,000 m. En este sentido, es necesario buscar tecnologías alternativas que sirvan de puente entre las medidas puntuales y las escalas intermedias. Esta tesis doctoral se basa en el uso de Fibra Óptica (FO) con sistema de medida de temperatura distribuida (DTS), una tecnología alternativa de reciente creación que ha levantado gran expectación en las últimas dos décadas. Específicamente utilizamos el método de fibra calentada, en inglés Actively Heated Fiber Optic (AHFO), en la cual los cables de Fibra Óptica se utilizan como sondas de calor mediante la aplicación de corriente eléctrica a través de la camisa de acero inoxidable, o de un conductor eléctrico simétricamente posicionado, envuelto, alrededor del haz de fibra óptica. El uso de fibra calentada se basa en la utilización de la teoría de los pulsos de calor, en inglés Heated Pulsed Theory (HPP), por la cual el conductor se aproxima a una fuente de calor lineal e infinitesimal que introduce calor en el suelo. Mediante el análisis del tiempo de ocurrencia y magnitud de la respuesta térmica ante un pulso de calor, es posible estimar algunas propiedades específicas del suelo, tales como el contenido de humedad, calor específico (C) y conductividad térmica. Estos parámetros pueden ser estimados utilizando un sensor de temperatura adyacente a la sonda de calor [método simple, en inglés single heated pulsed probes (SHPP)], ó a una distancia radial r [método doble, en inglés dual heated pulsed probes (DHPP)]. Esta tesis doctoral pretende probar la idoneidad de los sistemas de fibra óptica calentada para la aplicación de la teoría clásica de sondas calentadas. Para ello, se desarrollarán dos sistemas FO-DTS. El primero se sitúa en un campo agrícola de La Nava de Arévalo (Ávila, España), en el cual se aplica la teoría SHPP para estimar θ. El segundo sistema se desarrolla en laboratorio y emplea la teoría DHPP para medir tanto θ como C. La teoría SHPP puede ser implementada con fibra óptica calentada para obtener medidas distribuidas de θ, mediante la utilización de sistemas FO-DTS y el uso de curvas de calibración específicas para cada suelo. Sin embargo, la mayoría de aplicaciones AHFO se han desarrollado exclusivamente en laboratorio utilizando medios porosos homogéneos. En esta tesis se utiliza el programa Hydrus 2D/3D para definir tales curvas de calibración. El modelo propuesto es validado en un segmento de cable enterrado en una instalación de fibra óptica y es capaz de predecir la respuesta térmica del suelo en puntos concretos de la instalación una vez que las propiedades físicas y térmicas de éste son definidas. La exactitud de la metodología para predecir θ frente a medidas puntuales tomadas con sensores de humedad comerciales fue de 0.001 a 0.022 m3 m-3 La implementación de la teoría DHPP con AHFO para medir C y θ suponen una oportunidad sin precedentes para aplicaciones medioambientales. En esta tesis se emplean diferentes combinaciones de cables y fuentes emisoras de calor, que se colocan en paralelo y utilizan un rango variado de espaciamientos, todo ello en el laboratorio. La amplitud de la señal y el tiempo de llegada se han observado como funciones del calor específico del suelo. Medidas de C, utilizando esta metodología y ante un rango variado de contenidos de humedad, sugirieron la idoneidad del método, aunque también se observaron importantes errores en contenidos bajos de humedad de hasta un 22%. La mejora del método requerirá otros modelos más precisos que tengan en cuenta el diámetro del cable, así como la posible influencia térmica del mismo. ABSTRACT There is an increasing need to make the most efficient use of water for irrigation. A good approach to make irrigation as efficient as possible is to monitor soil water content (θ) using soil moisture sensors. Although, there is a broad range of different sensors and technologies, currently, none of them can practically and accurately provide vertical and lateral moisture profiles spanning 0-1 m depth and 0.1-1,000 m lateral scales. In this regard, further research to fulfill the intermediate scale and to bridge single-point measurement with the broaden scales is still needed. This dissertation is based on the use of Fiber Optics with Distributed Temperature Sensing (FO-DTS), a novel approach which has been receiving growing interest in the last two decades. Specifically, we employ the so called Actively Heated Fiber Optic (AHFO) method, in which FO cables are employed as heat probe conductors by applying electricity to the stainless steel armoring jacket or an added conductor symmetrically positioned (wrapped) about the FO cable. AHFO is based on the classic Heated Pulsed Theory (HPP) which usually employs a heat probe conductor that approximates to an infinite line heat source which injects heat into the soil. Observation of the timing and magnitude of the thermal response to the energy input provide enough information to derive certain specific soil thermal characteristics such as the soil heat capacity, soil thermal conductivity or soil water content. These parameters can be estimated by capturing the soil thermal response (using a thermal sensor) adjacent to the heat source (the heating and the thermal sources are mounted together in the so called single heated pulsed probe (SHPP)), or separated at a certain distance, r (dual heated pulsed method (DHPP) This dissertation aims to test the feasibility of heated fiber optics to implement the HPP theory. Specifically, we focus on measuring soil water content (θ) and soil heat capacity (C) by employing two types of FO-DTS systems. The first one is located in an agricultural field in La Nava de Arévalo (Ávila, Spain) and employ the SHPP theory to estimate θ. The second one is developed in the laboratory using the procedures described in the DHPP theory, and focuses on estimating both C and θ. The SHPP theory can be implemented with actively heated fiber optics (AHFO) to obtain distributed measurements of soil water content (θ) by using reported soil thermal responses in Distributed Temperature Sensing (DTS) and with a soil-specific calibration relationship. However, most reported AHFO applications have been calibrated under laboratory homogeneous soil conditions, while inexpensive efficient calibration procedures useful in heterogeneous soils are lacking. In this PhD thesis, we employ the Hydrus 2D/3D code to define these soil-specific calibration curves. The model is then validated at a selected FO transect of the DTS installation. The model was able to predict the soil thermal response at specific locations of the fiber optic cable once the surrounding soil hydraulic and thermal properties were known. Results using electromagnetic moisture sensors at the same specific locations demonstrate the feasibility of the model to detect θ within an accuracy of 0.001 to 0.022 m3 m-3. Implementation of the Dual Heated Pulsed Probe (DPHP) theory for measurement of volumetric heat capacity (C) and water content (θ) with Distributed Temperature Sensing (DTS) heated fiber optic (FO) systems presents an unprecedented opportunity for environmental monitoring. We test the method using different combinations of FO cables and heat sources at a range of spacings in a laboratory setting. The amplitude and phase-shift in the heat signal with distance was found to be a function of the soil volumetric heat capacity (referred, here, to as Cs). Estimations of Cs at a range of θ suggest feasibility via responsiveness to the changes in θ (we observed a linear relationship in all FO combinations), though observed bias with decreasing soil water contents (up to 22%) was also reported. Optimization will require further models to account for the finite radius and thermal influence of the FO cables, employed here as “needle probes”. Also, consideration of the range of soil conditions and cable spacing and jacket configurations, suggested here to be valuable subjects of further study and development.

Residual effect of natural and synthetic zinc chelates on zinc in a soil solution of a waterlogged acidic soil. Evolution of the pH and redox potential.

Zinc chelates have been widely used to correct deficiencies in this micronutrient in different soil types and under different moisture conditions. The aging of the metal in soil could cause a change in its availability. Over time the most labile forms of Zn could decrease in activity and extractability and change to more stable forms. Various soil parameters, such as redox conditions, time, soil type and moisture conditions, affect the aging process and modify the solubility of the metal. In general, redox conditions influence pH and also the chemical forms dissolved in the soil solution. Soil pH also affects Zn solubility; at high pH values, most of the Zn is present in forms that are not bioavailable to plants. The objective of this study was to determine the changes in Zn over time in a soil solution in a waterlogged acidic soil to which synthetic and natural chelates were applied

Nonlinear and Scaling Processes in Hydrology and Soil Science

Hydrology is the study of the properties, distribution and effects of water on the Earth?s soil, rocks and atmosphere. It also encompasses the study of the hydrologic cycle of precipitation, runoff, infiltration, storage, and evaporation, including the physical, biological and chemical reaction of water with the earth and its relation to life?.

Seasonal evolution of soil respiration in a mixed forestry plantation of walnuts (Juglans × intermedia Carr.) and alders (Alnus cordata (Loisel.) Duby) in Domaine de Restinclières (France)

The ecological intensification of crops is proposed as a solution to the growing demand of agricultural and forest resources, in opposition to intensive monocultures. The introduction of mixed cultures as mixtures between nitrogen fixing species and non nitrogen fixing species intended to increase crop yield as a result of an improvement of the available nitrogen and phosphorus in soil. Relationship between crops have received little attention despite the wide range of advantages that confers species diversity to these systems, such as increased productivity, resilience to disruption and ecological sustainability. Forests and forestry plantations can develop an important role in storing carbon in their tissues, especially in wood which become into durable product. A simplifying parameter to analyze the amount allocated carbon by plantation is the TBCA (total belowground carbon allocation), whereby, for short periods and mature plantations, is admitted as the subtraction between soil carbon efflux and litterfall. Soil respiration depends on a wide range of factors, such as soil temperature and soil water content, soil fertility, presence and type of vegetation, among others. The studied orchard is a mixed forestry plantation of hybrid walnuts(Juglans × intermedia Carr.) for wood and alders (Alnus cordata (Loisel.) Duby.), a nitrogen fixing specie through the actinomycete Frankia alni ((Woronin, 1866) Von Tubeuf 1895). The study area is sited at Restinclières, a green area near Montpellier (South of France). In the present work, soil respiration varied greatly throughout the year, mainly influenced by soil temperature. Soil water content did not significantly influence the response of soil respiration as it was constant during the measurement period and under no water stress conditions. Distance between nearest walnut and measurement was also a highly influential factor in soil respiration. Generally there was a decreasing trend in soil respiration when the distance to the nearest tree increased. It was also analyzed the response of soil respiration according to alder presence and fertilizer management (50 kg N·ha-1·año-1 from 1999 to 2010). None of these treatments significantly influenced soil respiration, although previous studies noticed an inhibition in rates of soil respiration under fertilized conditions and high rates of available nitrogen. However, treatments without fertilization and without alder presence obtained higher respiration rates in those cases with significant differences. The lack of significant differences between treatments may be due to the high coefficient of variation experienced by soil respiration measurements. Finally an asynchronous fluctuation was observed between soil respiration and litterfall during senescence period. This is possibly due to the slowdown in the emission of exudates by roots during senescence period, which are largely related to microbial activity.

Continuous multi-criteria methods for crop and soil conservation planning on La Colacha (Río Cuarto, Province of Cordoba, Argentina)

Agro-areas of Arroyos Menores (La Colacha) west and south of Rand south of R?o Cuarto (Prov. of Cordoba, Argentina) basins are very fertile but have high soil loses. Extreme rain events, inundations and other severe erosions forming gullies demand urgently actions in this area to avoid soil degradation and erosion supporting good levels of agro production. The authors first improved hydrologic data on La Colacha, evaluated the systems of soil uses and actions that could be recommended considering the relevant aspects of the study area and applied decision support systems (DSS) with mathematic tools for planning of defences and uses of soils in these areas. These were conducted here using multi-criteria models, in multi-criteria decision making (MCDM); first of discrete MCDM to chose among global types of use of soils, and then of continuous MCDM to evaluate and optimize combined actions, including repartition of soil use and the necessary levels of works for soil conservation and for hydraulic management to conserve against erosion these basins. Relatively global solutions for La Colacha area have been defined and were optimised by Linear Programming in Goal Programming forms that are presented as Weighted or Lexicographic Goal Programming and as Compromise Programming. The decision methods used are described, indicating algorithms used, and examples for some representative scenarios on La Colacha area are given.