S. K. Guru
4.3 Impact studies
aforementioned dataset, ARIMA (1,1,1) can be fitted. The fitted ARIMA (1,1,1) model without intercept is
ˆ . .
( . ) ( . )
Yt = −0 4435Yt 1− −0 9497 t 1−
0 1182 0 0615
ε (4.8)
The number in the bracket indicates the standard error of the parameter estimates.
Structural change refers to a long-term shift in the agricultural production. Over the last few decades, the structure of agri- cultural production around the world has been changing. The factors influencing this change have to be addressed.
Consider a dataset for two periods of time with Period I, say drought, having n1 observations, and Period II, say nor- mal, having n2 observations. Here, the objective is to find out whether there is any structural change or shift in the yield pat- tern between the drought and normal periods. Let there be two variables Y = productivity and X = area under cultivation and data were collected at two periods of time and given as follows:
Period I Period II
Productivity Area Productivity Area
1 2 1 2
2 4 3 4
2 6 3 6
4 10 5 8
6 13 6 10
6 12
7 14
9 16
9 18
11 20
To investigate this, the following models are defined:
Period I: Y = α1 + β1X + u (Drought) Period II: Y = α2 + β2X + u (Normal)
Here, the aim is to test α1 = α2 and β1 = β2. Test statistic
Let the number of restrictions be s. The test statistic is as follows:
F RSS RSS /s RSS / n p
r u
u
= −
−
( )
( )
which follows the F distribution with (s, n − p) d.f. RSSr is the residual sum of squares under null hypothesis and RSSu is the residual sum of squares under usual model (Waterman 1974).
A test for structural change
For Period I, the fitted model is
ˆY = −0.0625 0.4375X and RSS+ 1 = 0.6875 and for Period II the fitted model is
ˆY 0.4000 0.5091X and RSS= + 2 = 2.4727
Residual sum of squares (RSSu) = RSS1 + RSS2 = 3.1602 Residual sum of squares under null hypothesis (RSSr)
= 6.5565
F (6.5565 3.1602)/2 3.1602/(15 4) 5.91
= −
− =
It can be inferred that there is structural change in the yield pattern between drought and normal periods as F0.05 (2,11) = 3.98.
When the two samples are not independent, but the sample observations are paired together, then this test is applied. The paired observations are on the same unit or matching units. It is often used to compare ‘before’ and ‘after’ scores in experi- ments to determine whether significant change has occurred;
for example, to know the impact of climate change on a yield of perennial crops over years, assuming the rest of the variations as constant. Let (xi, yi), i = 1,…,n be the pairs of observations and let di = xi − yi. Our aim is to test H0 : μ1 = μ2.
Test statistic
t d
s / nd
=
follows t distribution with n − 1 d.f., where d=1/n∑in=1di and sd2 =1/(n 1)− ∑in=1(di−d)2.
Cluster analysis is a technique for grouping individuals or objects into unknown groups. In agriculture, cluster analysis has been used for diversity analysis, which is the classification of genotypes into arbitrary groups on the basis of their charac- teristics. In agro-meteorology, cluster analysis can be used to analyse historical records of the spatial and temporal variations in pest/insect populations in order to classify regions on the paired t-test for
assessing the impact
Cluster and discriminant analysis
basis of population densities and the frequency and persistence of outbreaks. The analysis can be used to improve regional monitoring and control of pest populations. Clustering tech- niques require that one define a measure of closeness or simi- larity between two observations. Clustering algorithms may be hierarchical or non-hierarchical. Hierarchical methods can be either agglomerative or divisive. An agglomerative hierarchical method starts with the individual objects, thus there are as many clusters as objects. The most similar objects are first grouped and these initial groups are merged according to their similari- ties. Eventually, as the similarity decreases, all sub-groups are fused into a single cluster.
Divisive hierarchical methods work in the opposite direction.
An initial single group of objects is divided into two sub-groups such that the objects in one sub-group are far from the objects in the others. These sub-groups are then further divided into dis- similar sub-groups. The process continues until there are as many sub-groups as objects, that is, until each object forms a group. The results of both an agglomerative and divisive method may be dis- played in the form of a two-dimensional diagram known as den- drogram, which illustrates the mergers or divisions that have been made at successive levels. K-means clustering is a popular non- hierarchical clustering technique. It begins with user-specified clusters and then reassigns data on the basis of the distance from the centroid of each cluster. See Johnson and Wichern (2006) and Hair et al. (2006) for more detailed explanations.
Discriminant analysis is a multi-variate technique concerned with classifying distinct set of objects (or set of observations) and with allocating new objects or observations to the previ- ously defined groups. It involves deriving variates, which are a combination of two or more independent variables that will dis- criminate best between a priori defined groups. The objectives of discriminant analysis are (i) identifying a set of variables that best discriminates between the groups, (ii) identifying a new axis, Z, such that new variables Z, given by the projec- tion of observations onto this new axis, provides the maximum separation or discrimination between the groups and (iii) clas- sifying future observations into one of the groups.
References
Box, G.E.P. and Jenkins, G.M. 1970. Time Series Analysis:
Forecasting and Control. Holden-Day, San Francisco.
Cox, D.R. 1958. The regression analysis of binary sequences (with dis- cussion). Journal of the Royal Statistical Society B, 20, 215–242.
Draper, N.R. and Smith, H. 1998. Applied Regression Analysis.
3rd ed., Wiley, New York.
Hair, J.F., Anderson R.E., Tatham, R.L. and Black, W.C. 2006. Multivariate Data Analysis. 5th ed., Pearson Education Inc, New Delhi, India.
Johnson, R.A. and Wichern, D.W. 2006. Applied Multivariate Statistical Analysis. 5th ed., Pearson Prentice Hall Inc., London.
Montgomery, D.C., Peck, E.C. and Vining, G. 2006.
Introduction to Linear Regression Analysis. 3rd ed., Wiley, New York.
Walker, S.H. and Duncan, D.B. 1967. Estimation of the probability of an event as a function of several independent variables. Biometrika, 54, 167–178.
Waterman, M.S. 1974. A restricted least squares problem.
Technometrics, 16, 135–138.
143
Nanotechnological interventions for mitigating global warming
Anjali Pande, Madhu Rawat, Rajeev Nayan, S.K. Guru and Sandeep Arora
Abstract
The rapidly changing climate, due to global warming, is a major cause of concern for agriculture scientists.
Undesirable climatic variability is bound to adversely affect the agricultural productivity, leading to food and nutritional insecurity for the burgeoning population.
Therefore, one of the biggest challenges is to augment Contents
Abstract 143
5.1 Introduction 144
5.2 Impact of climate change on crop production 145 5.3 Mitigation strategies for reducing crop
Productivity losses 146
5.4 Genetic engineering as a possible alternative 148
5.5 The Indian scenario 149
5.6 Nanotechnology as an alternative to GM crops 150
5.7 Nanotechnology in agriculture 152
5.8 Applications of nanotechnology 152
Crop improvement 152
5.9 Conclusion 156
Suggested reading 156
agricultural productivity, which is decreasing under envi- ronmental pressure. The scenario requires an intensive research for increased adaptation and devising novel strategies for mitigating the harmful effects of global warming on crop growth and productivity. Crop adapta- tion processes can be made more efficient and directed through targeted modifications of the cellular processes.
Nanotechnology offers a promising strategy for non-intru- sive engineering of crops under changing climatic condi- tions. Limitations faced by the conventional technologies in agriculture can be easily and efficiently addressed by means of this technology, with respect to the vulnerability to changing climatic conditions. Nanotechnology holds the potential to revolutionise agriculture and allied sys- tems, through the development of efficient nano-delivery systems, nano-fertilisers, nano-biosensors and so on, for increasing the growth and productivity. Direct as well as indirect nano-technological interventions, though still in their nascent stage, are bound to play a pivotal role in sus- tainable agricultural development under global warming.