Improving the management of water and nitrogen resources in cropping systems by using simulation models

Los modelos de simulación de cultivos permiten analizar varias combinaciones de laboreo-rotación y explorar escenarios de manejo. El modelo DSSAT fue evaluado bajo condiciones de secano en un experimento de campo de 16 años en la semiárida España central. Se evaluó el efecto del sistema de laboreo y las rotaciones basadas en cereales de invierno, en el rendimiento del cultivo y la calidad del suelo. Los modelos CERES y CROPGRO se utilizaron para simular el crecimiento y rendimiento del cultivo, mientras que el modelo DSSAT CENTURY se utilizó en las simulaciones de SOC y SN. Tanto las observaciones de campo como las simulaciones con CERES-Barley, mostraron que el rendimiento en grano de la cebada era mas bajo para el cereal continuo (BB) que para las rotaciones de veza (VB) y barbecho (FB) en ambos sistemas de laboreo. El modelo predijo más nitrógeno disponible en el laboreo convencional (CT) que en el no laboreo (NT) conduciendo a un mayor rendimiento en el CT. El SOC y el SN en la capa superficial del suelo, fueron mayores en NT que en CT, y disminuyeron con la profundidad en los valores tanto observados como simulados. Las mejores combinaciones para las condiciones de secano estudiadas fueron CT-VB y CT-FB, pero CT presentó menor contenido en SN y SOC que NT. El efecto beneficioso del NT en SOC y SN bajo condiciones Mediterráneas semiáridas puede ser identificado por observaciones de campo y por simulaciones de modelos de cultivos. La simulación del balance de agua en sistemas de cultivo es una herramienta útil para estudiar como el agua puede ser utilizado eficientemente. La comparación del balance de agua de DSSAT , con una simple aproximación “tipping bucket”, con el modelo WAVE más mecanicista, el cual integra la ecuación de Richard , es un potente método para valorar el funcionamiento del modelo. Los parámetros de suelo fueron calibrados usando el método de optimización global Simulated Annealing (SA). Un lisímetro continuo de pesada en suelo desnudo suministró los valores observados de drenaje y evapotranspiración (ET) mientras que el contenido de agua en el suelo (SW) fue suministrado por sensores de capacitancia. Ambos modelos funcionaron bien después de la optimización de los parámetros de suelo con SA, simulando el balance de agua en el suelo para el período de calibración. Para el período de validación, los modelos optimizados predijeron bien el contenido de agua en el suelo y la evaporación del suelo a lo largo del tiempo. Sin embargo, el drenaje fue predicho mejor con WAVE que con DSSAT, el cual presentó mayores errores en los valores acumulados. Esto podría ser debido a la naturaleza mecanicista de WAVE frente a la naturaleza más funcional de DSSAT. Los buenos resultados de WAVE indican que, después de la calibración, este puede ser utilizado como "benchmark" para otros modelos para periodos en los que no haya medidas de campo del drenaje. El funcionamiento de DSSAT-CENTURY en la simulación de SOC y N depende fuertemente del proceso de inicialización. Se propuso como método alternativo (Met.2) la inicialización de las fracciones de SOC a partir de medidas de mineralización aparente del suelo (Napmin). El Met.2 se comparó con el método de inicialización de Basso et al. (2011) (Met.1), aplicando ambos métodos a un experimento de campo de 4 años en un área en regadío de España central. Nmin y Napmin fueron sobreestimados con el Met.1, ya que la fracción estable obtenida (SOC3) en las capas superficiales del suelo fue más baja que con Met.2. El N lixiviado simulado fue similar en los dos métodos, con buenos resultados en los tratamientos de barbecho y cebada. El Met.1 subestimó el SOC en la capa superficial del suelo cuando se comparó con una serie observada de 12 años. El crecimiento y rendimiento del cultivo fueron adecuadamente simulados con ambos métodos, pero el N en la parte aérea de la planta y en el grano fueron sobreestimados con el Met.1. Los resultados variaron significativamente con las fracciones iniciales de SOC, resaltando la importancia del método de inicialización. El Met.2 ofrece una alternativa para la inicialización del modelo CENTURY, mejorando la simulación de procesos de N en el suelo. La continua emergencia de nuevas variedades de híbridos modernos de maíz limita la aplicación de modelos de simulación de cultivos, ya que estos nuevos híbridos necesitan ser calibrados en el campo para ser adecuados para su uso en los modelos. El desarrollo de relaciones basadas en la duración del ciclo, simplificaría los requerimientos de calibración facilitando la rápida incorporación de nuevos cultivares en DSSAT. Seis híbridos de maiz (FAO 300 hasta FAO 700) fueron cultivados en un experimento de campo de dos años en un área semiárida de regadío en España central. Los coeficientes genéticos fueron obtenidos secuencialmente, comenzando con los parámetros de desarrollo fenológico (P1, P2, P5 and PHINT), seguido de los parámetros de crecimiento del cultivo (G2 and G3). Se continuó el procedimiento hasta que la salida de las simulaciones estuvo en concordancia con las observaciones fenológicas de campo. Después de la calibración, los parámetros simulados se ajustaron bien a los parámetros observados, con bajos RMSE en todos los casos. Los P1 y P5 calibrados, incrementaron con la duración del ciclo. P1 fue una función lineal del tiempo térmico (TT) desde emergencia hasta floración y P5 estuvo linealmente relacionada con el TT desde floración a madurez. No hubo diferencias significativas en PHINT entre híbridos de FAO-500 a 700 , ya que tuvieron un número de hojas similar. Como los coeficientes fenológicos estuvieron directamente relacionados con la duración del ciclo, sería posible desarrollar rangos y correlaciones que permitan estimar dichos coeficientes a partir de la clasificación del ciclo. ABSTRACT Crop simulation models allow analyzing various tillage-rotation combinations and exploring management scenarios. DSSAT model was tested under rainfed conditions in a 16-year field experiment in semiarid central Spain. The effect of tillage system and winter cereal-based rotations on the crop yield and soil quality was evaluated. The CERES and CROPGRO models were used to simulate crop growth and yield, while the DSSAT CENTURY was used in the SOC and SN simulations. Both field observations and CERES-Barley simulations, showed that barley grain yield was lower for continuous cereal (BB) than for vetch (VB) and fallow (FB) rotations for both tillage systems. The model predicted higher nitrogen availability in the conventional tillage (CT) than in the no tillage (NT) leading to a higher yield in the CT. The SOC and SN in the top layer, were higher in NT than in CT, and decreased with depth in both simulated and observed values. The best combinations for the dry land conditions studied were CT-VB and CT-FB, but CT presented lower SN and SOC content than NT. The beneficial effect of NT on SOC and SN under semiarid Mediterranean conditions can be identified by field observations and by crop model simulations. The simulation of the water balance in cropping systems is a useful tool to study how water can be used efficiently. The comparison of DSSAT soil water balance, with a simpler “tipping bucket” approach, with the more mechanistic WAVE model, which integrates Richard’s equation, is a powerful method to assess model performance. The soil parameters were calibrated by using the Simulated Annealing (SA) global optimizing method. A continuous weighing lysimeter in a bare fallow provided the observed values of drainage and evapotranspiration (ET) while soil water content (SW) was supplied by capacitance sensors. Both models performed well after optimizing soil parameters with SA, simulating the soil water balance components for the calibrated period. For the validation period, the optimized models predicted well soil water content and soil evaporation over time. However, drainage was predicted better by WAVE than by DSSAT, which presented larger errors in the cumulative values. That could be due to the mechanistic nature of WAVE against the more functional nature of DSSAT. The good results from WAVE indicate that, after calibration, it could be used as benchmark for other models for periods when no drainage field measurements are available. The performance of DSSAT-CENTURY when simulating SOC and N strongly depends on the initialization process. Initialization of the SOC pools from apparent soil N mineralization (Napmin) measurements was proposed as alternative method (Met.2). Method 2 was compared to the Basso et al. (2011) initialization method (Met.1), by applying both methods to a 4-year field experiment in a irrigated area of central Spain. Nmin and Napmin were overestimated by Met.1, since the obtained stable pool (SOC3) in the upper layers was lower than from Met.2. Simulated N leaching was similar for both methods, with good results in fallow and barley treatments. Method 1 underestimated topsoil SOC when compared with a 12-year observed serial. Crop growth and yield were properly simulated by both methods, but N in shoots and grain were overestimated by Met.1. Results varied significantly with the initial SOC pools, highlighting the importance of the initialization procedure. Method 2 offers an alternative to initialize the CENTURY model, enhancing the simulation of soil N processes. The continuous emergence of new varieties of modern maize hybrids limits the application of crop simulation models, since these new hybrids should be calibrated in the field to be suitable for model use. The development of relationships based on the cycle duration, would simplify the calibration requirements facilitating the rapid incorporation of new cultivars into DSSAT. Six maize hybrids (FAO 300 through FAO 700) were grown in a 2-year field experiment in a semiarid irrigated area of central Spain. Genetic coefficients were obtained sequentially, starting with the phenological development parameters (P1, P2, P5 and PHINT), followed by the crop growth parameters (G2 and G3). The procedure was continued until the simulated outputs were in good agreement with the field phenological observations. After calibration, simulated parameters matched observed parameters well, with low RMSE in most cases. The calibrated P1 and P5 increased with the duration of the cycle. P1 was a linear function of the thermal time (TT) from emergence to silking and P5 was linearly related with the TT from silking to maturity . There were no significant differences in PHINT between hybrids from FAO-500 to 700 , as they had similar leaf number. Since phenological coefficients were directly related with the cycle duration, it would be possible to develop ranges and correlations which allow to estimate such coefficients from the cycle classification.

Programs for management of water withdrawals in Illinois : final report /

"Project: 88/062."

The contribution and status of physical removal in sustainable management of water hyacinth

Physical control of water hyacinth consists of removing the plants from the water by hand or machines. It is considered over effetive because it involves removing the whole plants from water. The first attempt on physical control was in 1992 when weed infestation was causing serious problems to the fishing communities in Lake Kyoga. The fishermen had problems of accessing the lake as huge masses of mobile weed blocked landing sites. Furthermore, the fishers lost their nets, which were swept away by mobile water hyacinth. As a result, an integrated control strategy involving physical control (manual and mechanical removal) was put in place. Through this method, the fishers were able to open up access routes to fishing grounds even though weed mats often reblocked the access routes. In the infested lakes, manual removal offered remedial relief to fish Iandings and other access sites. Sites of strategic importance such as hydro-electric power generation dam, water intake points and docking points which had large masses of water hyacinth required heavy machinery and mechanical harvesters were used at these sites.

On Real-Time Monitoring And Control For Efficient Management Of Drinking Water Networks: Barcelona Case Study

Drinking water utilities in urban areas are focused on finding smart solutions facing new challenges in their real-time operation because of limited water resources, intensive energy requirements, a growing population, a costly and ageing infrastructure, increasingly stringent regulations, and increased attention towards the environmental impact of water use. Such challenges force water managers to monitor and control not only water supply and distribution, but also consumer demand. This paper presents and discusses novel methodologies and procedures towards an integrated water resource management system based on advanced ICT technologies of automation and telecommunications for largely improving the efficiency of drinking water networks (DWN) in terms of water use, energy consumption, water loss minimization, and water quality guarantees. In particular, the paper addresses the first results of the European project EFFINET (FP7-ICT2011-8-318556) devoted to the monitoring and control of the DWN in Barcelona (Spain). Results are split in two levels according to different management objectives: (i) the monitoring level is concerned with all the aspects involved in the observation of the current state of a system and the detection/diagnosis of abnormal situations. It is achieved through sensors and communications technology, together with mathematical models; (ii) the control level is concerned with computing the best suitable and admissible control strategies for network actuators as to optimize a given set of operational goals related to the performance of the overall system. This level covers the network control (optimal management of water and energy) and the demand management (smart metering, efficient supply). The consideration of the Barcelona DWN as the case study will allow to prove the general applicability of the proposed integrated ICT solutions and their effectiveness in the management of DWN, with considerable savings of electricity costs and reduced water loss while ensuring the high European standards of water quality to citizens.

Perceptions of water conditions and management in the Sonora River Basin, Sonora, Mexico

The effects of climate change are expected to be very severe in arid regions. The Sonora River Basin, in the northwestern state of Sonora, Mexico, is likely to be severely affected. Some of the anticipated effects include precipitation variability, intense storm events, higher overall temperatures, and less available water. In addition, population in Sonora, specifically the capital city of Hermosillo, is increasing at a 1.5% rate and current populations are near 700,000. With the reduction in water availability and an increase in population, Sonora, Mexico is expected to experience severe water resource issues in the near future. In anticipation of these changes, research is being conducted in an attempt to improve water management in the Sonora River Basin, located in the northwestern part of Sonora. This research involves participatory modeling techniques designed to increase water manager awareness of hydrological models and their use as integrative tools for water resource management. This study was conducted as preliminary research for the participatory modeling grant in order to gather useful information on the population being studied. This thesis presents research from thirty-four in-depth interviews with water managers, citizens, and agricultural producers in Sonora, Mexico. Data was collected on perceptions of water quantity and quality in the basin, thoughts on current water management practices, perceptions of climate change and its management, experience with, knowledge of, and trust in hydrological models as water management tools. Results showed that the majority of interviewees thought there was not enough water to satisfy their daily needs. Most respondents also agreed that the water available was of good quality, but that current management of water resources was ineffective. Nearly all interviewees were aware of climate change and thought it to be anthropogenic. May reported experiencing higher temperatures, precipitation changes, and higher water scarcity and attributed those fluctuations to climate change. 65% of interviewees were at least somewhat familiar with hydrological models, though only 28% had ever used them or their output. Even with model usage results being low, 100% of respondents believed hydrological models to be very useful water management tools. Understanding how water, climate change, and hydrological models are perceived by this population of people is essential to improving their water management practices in the face of climate change.

An example of integration between en economic and an hydrologic model in the framework of water resource management problems

Growing scarcity, increasing demand and bad management of water resources are causing weighty competition for water and consequently managers are facing more and more pressure in an attempt to satisfy users? requirement. In many regions agriculture is one of the most important users at river basin scale since it concentrates high volumes of water consumption during relatively short periods (irrigation season), with a significant economic, social and environmental impact. The interdisciplinary characteristics of related water resources problems require, as established in the Water Framework Directive 2000/60/EC, an integrated and participative approach to water management and assigns an essential role to economic analysis as a decision support tool. For this reason, a methodology is developed to analyse the economic and environmental implications of water resource management under different scenarios, with a focus on the agricultural sector. This research integrates both economic and hydrologic components in modelling, defining scenarios of water resource management with the goal of preventing critical situations, such as droughts. The model follows the Positive Mathematical Programming (PMP) approach, an innovative methodology successfully used for agricultural policy analysis in the last decade and also applied in several analyses regarding water use in agriculture. This approach has, among others, the very important capability of perfectly calibrating the baseline scenario using a very limited database. However one important disadvantage is its limited capacity to simulate activities non-observed during the reference period but which could be adopted if the scenario changed. To overcome this problem the classical methodology is extended in order to simulate a more realistic farmers? response to new agricultural policies or modified water availability. In this way an economic model has been developed to reproduce the farmers? behaviour within two irrigation districts in the Tiber High Valley. This economic model is then integrated with SIMBAT, an hydrologic model developed for the Tiber basin which allows to simulate the balance between the water volumes available at the Montedoglio dam and the water volumes required by the various irrigation users.

Modeling Equitable Distribution of Water: Dynamic Inversion-Based Controller Approach

It is a well-known fact that most of the developing countries have intermittent water supply and the quantity of water supplied from the source is also not distributed equitably among the consumers. Aged pipelines, pump failures, and improper management of water resources are some of the main reasons for it. This study presents the application of a nonlinear control technique to overcome this problem in different zones in the city of Bangalore. The water is pumped to the city from a large distance of approximately 100km over a very high elevation of approximately 400m. The city has large undulating terrain among different zones, which leads to unequal distribution of water. The Bangalore, inflow water-distribution system (WDS) has been modeled. A dynamic inversion (DI) nonlinear controller with proportional integral derivative (PID) features (DI-PID) is used for valve throttling to achieve the target flows to different zones of the city. This novel approach of equitable water distribution using DI-PID controllers that can be used as a decision support system is discussed in this paper.

Eutrophication and the management of planktonic algae: What Vollenweider couldn't tell us

The ”Vollenweider model” is a sophisticated mathematical statement about the long-range behaviour of (mainly temperate) lakes and their ability to support phytoplankton chlorophyll. Misapplication of the model, against which Vollenweider himself warned, has led to many misconceptions about the dynamics of plankton in lakes and reservoirs and about how best to manage systems subject to eutrophication. This contribution intends to frame the most important issues in context of the phosphorus- loading and phosphorus-limitation concepts. Emphasis is placed on the need to distinguish rate-limitation from capacity-limitation, to understand which is more manageable and why, to discern the mechanisms of internal recycling and their importance, and to appreciate the respective roles of physical and biotic components in local control of algal dynamics. Some general approaches to the management of water quality in lakes and reservoirs to eutrophication are outlined.

Development Of Water Pollution Early Warning System For Oyster Harvesting Areas

The objective of this study is to develop a Pollution Early Warning System (PEWS) for efficient management of water quality in oyster harvesting areas. To that end, this paper presents a web-enabled, user-friendly PEWS for managing water quality in oyster harvesting areas along Louisiana Gulf Coast, USA. The PEWS consists of (1) an Integrated Space-Ground Sensing System (ISGSS) gathering data for environmental factors influencing water quality, (2) an Artificial Neural Network (ANN) model for predicting the level of fecal coliform bacteria, and (3) a web-enabled, user-friendly Geographic Information System (GIS) platform for issuing water pollution advisories and managing oyster harvesting waters. The ISGSS (data acquisition system) collects near real-time environmental data from various sources, including NASA MODIS Terra and Aqua satellites and in-situ sensing stations managed by the USGS and the NOAA. The ANN model is developed using the ANN program in MATLAB Toolbox. The ANN model involves a total of 6 independent environmental variables, including rainfall, tide, wind, salinity, temperature, and weather type along with 8 different combinations of the independent variables. The ANN model is constructed and tested using environmental and bacteriological data collected monthly from 2001 – 2011 by Louisiana Molluscan Shellfish Program at seven oyster harvesting areas in Louisiana Coast, USA. The ANN model is capable of explaining about 76% of variation in fecal coliform levels for model training data and 44% for independent data. The web-based GIS platform is developed using ArcView GIS and ArcIMS. The web-based GIS system can be employed for mapping fecal coliform levels, predicted by the ANN model, and potential risks of norovirus outbreaks in oyster harvesting waters. The PEWS is able to inform decision-makers of potential risks of fecal pollution and virus outbreak on a daily basis, greatly reducing the risk of contaminated oysters to human health.

Effect of water management practice on pesticide behavior in paddy water

The fate and transport of three herbicides commonly used in rice production in Japan were compared using two water management practices. The herbicides were simetryn, thiobencarb and mefenacet. The first management practice was an intermittent irrigation scheme using an automatic irrigation system (AI) with a high drainage gate and the second one was a continuous irrigation and overflow drainage scheme (CI) in experimental paddy fields. Dissipation of the herbicides appeared to follow first order kinetics with the half-lives (DT₅₀) of 1.6-3.4 days and the DT₉₀ (90% dissipation) of 7.4-9.8 days. The AI scheme had little drainage even during large rainfall events thus resulting in losses of less than 4% of each applied herbicide through runoff. Meanwhile the CI scheme resulted in losses of about 37%, 12% and 35% of the applied masses of simetryn, thiobencarb and mefenacet, respectively. The intermittent irrigation scheme using an automatic irrigation system with a high drainage gate saved irrigation water and prevented herbicide runoff whereas the continuous irrigation and overflow scheme resulted in significant losses of water as well as the herbicides. Maintaining the excess water storage is important for preventing paddy water runoff during significant rainfall events. The organic carbon partition coefficient K_oc seems to be a strong indicator of the aquatic fate of the herbicide as compared to the water solubility (S_W). However, further investigations are required to understand the relation between K_oc and the agricultural practices upon the pesticide fate and transport. An extension of the water holding period up to 10 days after herbicide application based on the DT₉₀ from the currently specified period of 3-4 days in Japan is recommended to be a good agricultural practice for controlling the herbicide runoff from paddy fields. Also, the best water management practice, which can be recommended for use during the water holding period, is the intermittent irrigation scheme using an automatic irrigation system with a high drainage gate. © 2006 Elsevier B.V. All rights reserved.

Fuzzy optimization model for water quality management of a river system - Closure

A fuzzy waste-load allocation model, FWLAM, is developed for water quality management of a river system using fuzzy multiple-objective optimization. An important feature of this model is its capability to incorporate the aspirations and conflicting objectives of the pollution control agency and dischargers. The vagueness associated with specifying the water quality criteria and fraction removal levels is modeled in a fuzzy framework. The goals related to the pollution control agency and dischargers are expressed as fuzzy sets. The membership functions of these fuzzy sets are considered to represent the variation of satisfaction levels of the pollution control agency and dischargers in attaining their respective goals. Two formulations—namely, the MAX-MIN and MAX-BIAS formulations—are proposed for FWLAM. The MAX-MIN formulation maximizes the minimum satisfaction level in the system. The MAX-BIAS formulation maximizes a bias measure, giving a solution that favors the dischargers. Maximization of the bias measure attempts to keep the satisfaction levels of the dischargers away from the minimum satisfaction level and that of the pollution control agency close to the minimum satisfaction level. Most of the conventional water quality management models use waste treatment cost curves that are uncertain and nonlinear. Unlike such models, FWLAM avoids the use of cost curves. Further, the model provides the flexibility for the pollution control agency and dischargers to specify their aspirations independently.

Adaptation and management of Australian buffalograss cultivars for shade and water conservation

Soft-leaf buffalo grass is increasing in popularity as an amenity turfgrass in Australia. This project was instigated to assess the adaptation of and establish management guidelines for its use in Australias vast array of growing environments. There is an extensive selection of soft-leaf buffalo grass cultivars throughout Australia and with the countrys changing climates from temperate in the south to tropical in the north not all cultivars are going to be adapted to all regions. The project evaluated 19 buffalo grass cultivars along with other warm-season grasses including green couch, kikuyu and sweet smother grass. The soft-leaf buffalo grasses were evaluated for their growth and adaptation in a number of regions throughout Australia including Western Australia, Victoria, ACT, NSW and Queensland. The growth habit of the individual cultivars was examined along with their level of shade tolerance, water use, herbicide tolerance, resistance to wear, response to nitrogen applications and growth potential in highly alkaline (pH) soils. The growth habit of the various cultivars currently commercially available in Australia differs considerably from the more robust type that spreads quicker and is thicker in appearance (Sir Walter, Kings Pride, Ned Kelly and Jabiru) to the dwarf types that are shorter and thinner in appearance (AusTine and AusDwarf). Soft-leaf buffalo grass types tested do not differ in water use when compared to old-style common buffalo grass. Thus, soft-leaf buffalo grasses, like other warm-season turfgrass species, are efficient in water use. These grasses also recover after periods of low water availability. Individual cultivar differences were not discernible. In high pH soils (i.e. on alkaline-side) some elements essential for plant growth (e.g. iron and manganese) may be deficient causing turfgrass to appear pale green, and visually unacceptable. When 14 soft-leaf buffalo grass genotypes were grown on a highly alkaline soil (pH 7.5-7.9), cultivars differed in leaf iron, but not in leaf manganese, concentrations. Nitrogen is critical to the production of quality turf. The methods for applying this essential element can be manipulated to minimise the maintenance inputs (mowing) during the peak growing period (summer). By applying the greatest proportion of the turfs total nitrogen requirements in early spring, peak summer growth can be reduced resulting in a corresponding reduction in mowing requirements. Soft-leaf buffalo grass cultivars are more shade and wear tolerant than other warm-season turfgrasses being used by homeowners. There are differences between the individual buffalo grass varieties however. The majority of types currently available would be classified as having moderate levels of shade tolerance and wear reasonably well with good recovery rates. The impact of wear in a shaded environment was not tested and there is a need to investigate this as this is a typical growing environment for many homeowners. The use of herbicides is required to maintain quality soft-leaf buffalo grass turf. The development of softer herbicides for other turfgrasses has seen an increase in their popularity. The buffalo grass cultivars currently available have shown varying levels of susceptibility to the chemicals tested. The majority of the cultivars evaluated have demonstrated low levels of phytotoxicity to the herbicides chlorsulfuron (Glean) and fluroxypyr (Starane and Comet). In general, soft leaf buffalo grasses are varied in their makeup and have demonstrated varying levels of tolerance/susceptibility/adaptation to the conditions they are grown under. Consequently, there is a need to choose the cultivar most suited to the environment it is expected to perform in and the management style it will be exposed to. Future work is required to assess how the structure of the different cultivars impacts on their capacity to tolerate wear, varying shade levels, water use and herbicide tolerance. The development of a growth model may provide the solution.