Submitted To:-  Dr. P.M. Patel  Assistant Research Scientist  Main Forage Research Station  AAU, Anand,Gujarat Submitted By:-  Sibananda Khatai  Reg. no.:  Msc. (Agricultural Statistics)

Introduction Permanent grasslands, used either for forage production from meadows or as pastures, make up a significant proportion in India. variation in seasonal harvested dry matter (DM) production is quite common while the variation between individual cuts is much greater. Most of this variability in forage DM production is caused by weather factors and their interaction with soil conditions, sward composition and management.

A model is a schematic representation of the conception of a system or an act of mimicry or a set of equations, which represents the behavior of a system. TYPES OF MODELS Depending upon the purpose for which it is designed the models are classified into different groups or types. Of them a few are : a. Statistical empirical models: These models express the relationship between yield or yield components and weather parameters. In these models relationships are measured in a system using statistical techniques. Example: Step wise regressions, correlation, etc. Actual mechanism of processes is not disclosed b. Mechanistic models: These models explain not only the relationship between weather parameters and yield, but also the mechanism of these models (explains the relationship of influencing dependent variables). These models are based on physical selection. mechanism of the processes involved is discussed e.g. photosynthesis based model. C.Deterministic models: These models estimate the exact value of the yield or dependent variable. These models also have defined coefficients. In which a definite output is given e.g. NPK doses are applied and the definite yields are given out.

d. Stochastic models: A probability element is attached to each output. For each set of inputs different outputs are given along with probabilities. These models define yield or state of dependent variable at a given rate. The models are based on the probability of occurrence of some event or external variable. e. Dynamic models: These models predict changes in crop status with time. Time is included as a variable. Both dependent and independent variables are having values which remain constant over a given period of time. f. Static: Time is not included as a variables. Dependent and independent variables having values remain constant over a given period of time. Time is not a factor. g. Simulation models: Computer models, in general, are a mathematical representation of a real world system. One of the main goals of crop simulation models is to estimate agricultural production as a function of weather and soil conditions as well as crop management. These models use one or more sets of differential equations, and calculate both rate and state variables over time, normally from planting until harvest maturity or final harvest.`

h. Descriptive model: A descriptive model defines the behaviour of a system in a simple manner. The model reflects little or none of the mechanisms that are the causes of phenomena. But, consists of one or more mathematical equations. An example of such an equation is the one derived from successively measured weights of a crop. The equation is helpful to determine quickly the weight of the crop where no observation was made. i.Explanatory model: This consists of quantitative description of the mechanisms and processes that cause the behaviour of the system. To create this model, a system is analyzed and its processes and mechanisms are quantified separately. The model is built by integrating these descriptions for the entire system. It contains descriptions of distinct processes such as leaf area expansion, tiller production, etc. Crop growth is a consequence of these processes.

A number of models dealing with various agronomical and ecological aspects of grassland have been developed in the past decades models used to study the interactions between soil and weather conditions, and management and crop growth, thereby facilitating harvest decisions that require optimization of forage yield and nutritive value main advantages of crop model application is the possibility to use the models under various weather and soil conditions and in various environments in various regions of the world

The statistical techniques used in designing the models are as follows: 1. Simple regression analysis 2. Simple correlation technique. 3. Curvilinear correlations techniques 4. Multiple regression analysis 5. Stepwise regression analysis 6. Fishers orthogonal polynomial techniques 7. Mallow’s Cp techniques. 8. Marko chain model.

Grassland Statistical Model(GRAM) In addition to comparison of the estimated vs. observed values for the amount of forage DM produced, both GRAM-R and GRAM-N versions were evaluated with respect to the production of patterns in residuals against N fertilizer application rate, year, cut number, location, length of the growing season, date of the previous cut. It was found that, with the GRAM-N or GRAM-R methodology, up to 0.78% of the variability in harvested herbage DM production could be explained with a systematic bias of %. The models showed stable performance over subsets of dry and wet years.

Generalized GRAM models were also successfully used to estimate daily herbage growth during the season, explaining between 0.63 and 0.91 of variability in individual cases. It was possible to issue a probabilistic forecast of the harvestable herbage DM production early in the season with reasonable accuracy. The results showed that the GRAM model could be used instead of (or in parallel with) more sophisticated grassland models in areas or sites where complete data sets are not yet available

Evapotranspiration model 1. One of the most critical parameters frequently used to characterize growing conditions of field and forage crops is evapotranspiration (ET). 2.In recent decades, the theoretical and applied analysis of this biophysical phenomenon has received much attention (Hatfield, 1988; Monteith and Unsworth, 1990). After reviewing several models for estimating ET, the Penman–Monteith model (Monteith, 1965), as presented by Allen et al. (1998), was found to be a reliable method for predicting ETp orreference evapotranspiration (ETr). 3. It is defined as evapotranspiration from short grass maintained under optimum soil water content and nutritional conditions and is calculated on a daily basis.

4. The simplified Food and Agriculture Organisation (FAO) method (Allenet al., 1998) also includes daily water balance of the lower rooted layer and allows calculation not only of ETr but also of the value of the actual evapotranspiration (ETa) and soil water content. 5. It was found that the FAO method explained over 0.70 of the daily fluctuation in soil water content at depths of 20 and 40 cm where 0.90 of the root mass is concentrated. This is consistent with the results of similar models (e.g. Woodward et al., 2001) and confirms that the weekly ETa total closely fits soil water loss from water balance.

Design of the statistical model The grassland statistical model (GRAM), which could be applied both to meadows and grazed grasslands. The model itself is based on the modified approach originally used by Han et al. (2003). The GRAM assumes that grass growth depends on the soil water content in the active root zone as well as water stored in the plant tissues. Therefore, the water balance is a significant factor in canopy development. The GRAM further supposes that all of the supply of water can be attributed to rainfall Water uptake is then divided mainly between the plant transpiration and the soil evaporation, with adjustments for surface runoff, drainage and interception.

The stepwise regression procedure of the UNISTAT 5.1 statistical package (UNISTAT Ltd, London, UK) was used for analysis of the calibration data subset. The models with the highest variability explained and the lowest mean square errors were regarded as the most accurate. The best set of equations for a given data subset is referred to as grassland statistical model – multiple regression (or GRAM-R). In the second step, this model used to calculate the amount of harvested DM of herbage for the verification subset and compared with the experimental results. The same set of independent variables was used to derive grassland statistical model – neural networks version (GRAM-N)

The aim also to quantify the relationship between the set of independent variables that included effective accumulated temperature, effective accumulated solar radiation, duration of growth under each particular cutting, mineral N application, cut number. Polynomial regression function and neural-network-based methods were used to derive the relationship between the set of independent variables and the amount of harvested DM of forage set as the dependent variable.

LINGRA-N model objective is to develop a tool that is sensitive to climatic variation, soil properties and management practices for simulating and evaluating the growth and herbage yield of sown or permanent grasslands. The LINGRA model (Bouman et al., 1996; Schapendonk et al., 1998; Wolf, 2006; Pogačar andKajfež-Bogataj, 2011) is an intermediate type of model in which both static and dynamic descriptions are used.

To calculate the grassland herbage yield (g dry matter m-2) can be calculated by multiplying total biomass by dynamic grass specific partitioning factors, Y=∫(f t PAR t E t ) HI Where f t is the fraction of photosynthetically active radiation (PAR) intercepted by the foliage, PAR t the incoming amount of PAR (MJ m -2 d -1 ), and Et is the light utilisation efficiency(g dry matter (MJ PAR)-1).

REVIEW OF LITERATURE Scatterplots of the observed versus model predicted herbage yield for two grass species on the same location (Jablje). Left: cock’s foot (DG), right: perennial ryegrass (LP) Tjaša POGAČAR et al

The herbage yield of cock’s foot in Jablje: average (observed yield), minimum (min) and maximum (max) values of observed herbage yield, the default output of the model without calibration (default), 1st, 2nd, and 6 th step herbage yield results of the calibration procedure, and model predicted herbage yield at the end of calibration

Conclusions 1. productivity of forages is highly dependent on available soil water, global radiation, air temperature, applied N and management 2.These factors explain up to 0.78 of the variability in herbage mass and are useful in determining the production potential of selected sites. 3.The GRAM has proved to be a suitable tool that takes these strong links into account and may thus be used for various practical purposes, with no significant difference between GRAM-R and GRAM-N approaches.

3. It has been shown that the GRAM versions are capable of reproducing herbage accumulation variation during extreme seasons 4. complexity of LINGRA-N construction is appropriate for its intended application 5. LINGRA-N calibrated model for the simulation of the herbage yield of grass monocultures under various weather conditions

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