eChapters

Snow is precipitation of solid water, mainly in the form of branched hexagonal crystals or stars. It is “precipitation of white opaque grains of ice”. Measurement of snow cover is related to runoff estimation and also important for hilly agriculture.

4.1. Snowfall

It is the amount of fresh snow deposited over a specified period (generally 24 hours). The measurements relate to depth and water content of the snowfall.

The information on soil-water content is necessary from the point of view of efficient water management of crop production as water required by crops is to be met from the water stored in their root zone. Soil water content changes periodically as a result of changes in field water balance components namely, precipitation, irrigation, evapotranspiration, runoff and deep percolation. Crop growth is adversely affected if the soil water depletes below certain level. For selection of crops, deciding of irrigation level and frequency of irrigation, the assessment of water content of soil is important.

Water is an important input in crop production. It acts as solvent, reactant and used for transpiration and maintaining cell turgidity. Hence, knowledge of soil moisture is essential for making irrigation scheduling. For determining soil moisture status, the commonly used methods and instruments are discussed along with their advantages and disadvantages. The soil moisture can be measured by determining either the soil water content or the soil water potential. The measurement of soil water content is an estimation of the mass or volume of water in the soil, while the soil water potential is an expression of the soil water energy status. The relation between content and potential is not universal and depends on the characteristics of the local soil, such as soil density and soil texture. We can measure soil moisture content both by direct and indirect methods. In direct method, we remove the water from the soil sample by evaporation and the amount removed is determined. This method is popularly known as gravimetric method. We measure property of soil that is affected by soil water content under the indirect methods. Indirect methods employ tensiometric, nuclear (neutron and gamma radiations), electromagnetic (radar and time domain reflectometers), hygrometric (electrical resistance, capacitance, Infrared absorption) techniques besides remote sensing for making soil water models. In the following paragraphs both the methods of soil water measurement has been discussed.

Tensiometer is a device to measure soil moisture tension or equivalent negative pressure of water in the soil. A tensiometer consists of a tube sealed at one end by a porous ceramic cup which is in contact with the soil and a vacuum gauge or a manometer connected at the other end above the soil surface. When the tensiometer is filled with water, the manometer or gauge will read zero tension. When such a tensiometer is placed in an unsaturated soil, the soil in contact with the porous ceramic cup will immediately start sucking water through the porous cup wall. The water in the soil pores immediately establishes hydraulic equilibrium with the water in the cup through saturated pores of the cup wall. Water and solutes can f low through the pores of the cup wall but not the air within the working range of the tensiometer. Water could be sucked from the tensiometer by the soil until vacuum created inside the tensiometer is just sufficient to overcome the suction of the soil. At equilibrium, the tensiometer reads directly the amount of soil suction. The outf low of water from the cup is very little. The effective range of the tensiometer is 0 to 0.85 bars depending on quality of the porous cup.

The measurement of soil moisture is needed to determine when to irrigate and the amount of water needed when irrigating, to evaluate evapotranspiration, and to monitor soil matric potential. The soil moisture is measured in two ways- direct and indirect methods as follows:

The surface of the earth gets heated up during the day and gets cooled during the night causing diurnal changes in the top layers of the soil. Soil temperature is an important part of micro-environment, where plant roots grow and capture the water and nutrients and thus, it affects the plant growth and yield. During crop germination also soil temperatures play vital role. Since the heat regimes of these layers are governed by the soil temperature, the measurement of soil temperature becomes extremely important.

Soil temperature plays an important role in plant growth. Solar radiation received on the earth surface raises the temperature of the soil surface from morning to solar noon followed by a decline until the next morning. Soil temperature gradients established on the surface lead to flow of heat downwards causing a rise in temperature of lower layers. These variations in temperature affect germination, emergence and further growth of plants. Several types of thermometers such as mercury or liquid in glass, bimetallic, bourdon gauge, thermocouples and electrical resistance have been used in soil research but the use of thermocouples and thermistors has been found most useful. A brief description of different types of thermometers used in measurement of soil temperature is given below:

Liquids in Glass Thermometer

A liquid-in-glass thermometer (Figure 20.1) consists of a capillary glass tube with a bulb at one end filled with a thermometric liquid (mercury), vacuumed and sealed. By reading the position of the liquid level on a scale the temperature value can be obtained.

The solar energy is the main source of energy for the processes occurring at the earth surface and in its atmosphere. Crop production, is in fact an exploitation of solar radiation and plants are the converters of solar energy into a useful form of energy which is biomass and sustain life providing food, fodder, fiber, fuel, fruits etc. Sun energy fulfills two essential needs of the plants i.e.  (i) light for photosynthesis including many other photo processes and functions of the plants, (ii) thermal conditions required for the normal physiological functions of the plant. Thus, the crop production and agriculture is basically dependent on quality and quantity of radiation.

Water loss from a plant in the form of vapour is known as transpiration. Loss of water vapour mainly from leaf cells through pores but also from the leaf cuticle and through lenticels of the stem. The resistance to diffusion of water vapour through a plant’s stomata is called as stomatal resistance. Whereas, stomatal conductance is a numerical measure of the maximum rate of passage of either water vapour or carbon dioxide through the stomata, or small pores of the plant.

Weather phenomena are not localized, it moves and varies over space and time. The weather over a place or area is the result of far away weather events/conditions. Acquisition of global scale observation, therefore, becomes a pre-requisite for understanding the physics of the weather and also to represent the weather condition over an area at a particular time. Complex three-dimensional models of weather systems can be made by collecting weather data at multiple levels in the atmosphere. Upper-air data are important to know present weather over a place and crucial for weather forecasting.

Wind influences the plant life both physiologically and mechanically. Wind affects plant directly by increasing the transpiration and intake of CO₂. Thus raising the supply of CO₂ to the plants and thereby increase in photosynthesis. However, the increase in photosynthesis is again upto a certain wind speed beyond which its rate become constant. The warm and dry winds increase evaporative loss and cause moisture stress. Lodging is one of severe injury caused by strong winds which causes great yield loss depending upon the stage of crop. This injury is common in paddy, maize, wheat, sorghum and sugarcane. Strong winds damage fruit trees extensively by breaking leaves and twigs and causing fruit drops.

4.1 Learning Objectives
By the end of this chapter, you will be able to:
i) Understand the concepts of Central Tendency and Partition Values;
ii) Identify appropriate measures for different data sets;
iii) Distinguish between different types of means;
iv) Apply Partition Values in data analysis.

4.2 Introduction

Nowadays, the ability to proficiently analyze and interpret data sets is indispensable for strategic decision-making. This chapter, ‘Measures of Central Tendency and Partition Values,’ extends beyond the basics of mean, median, and mode to explore the deeper layers of data analysis through quartiles, deciles, and percentiles. These measures offer a more comprehensive understanding of data distribution, crucial for identifying trends and making precise business predictions. We will unravel how these statistical tools can be effectively employed to dissect and interpret complex data sets, providing business professionals with an enhanced toolkit for informed analysis and decision-making in various business scenarios.

3.1 MEASURES OF CENTRAL TENDENCY (AVERAGES)

When data are presented in raw form or in the form of frequency distribution, they fail to provide a general idea of the data under study. The general idea of statistical methods is to condense the raw data into a form that can convey some meaningful characteristic(s) of the data. Though classification simplifies the data and improves the understanding of the main characteristics in the data, it is still difficult to remember. In any distribution of data, values of a variable may tend to cluster (or concentrate) around a central value. The data must be condensed into a single value. Such presentation of data is called a Central Tendency and the measures devised to consider this tendency are known as Measures of Central Tendency.

An average condenses a frequency distribution or raw data and presents it in a single representative number. It is that single value which is considered as the most representative or typical value for a set of values. Such a value usually lies somewhere near the centre of the group. That is why, an average is usually referred to as a measure of central tendency. It is located at a point around which most of the other values tend to cluster and therefore it is also termed as a measure of central location.

3.1 Introduction

One of the most important objectives of statistical analysis is to summaries the information contained in the data which may be considered either as a population or as a sample (or sub-population). If the set of data consists of all conceivably possible (or hypothetically possible) observations of a certain phenomenon or a variable, we call it as population. If a set of data contains only a part of these observations, that is selected values of a variable, we call it as sample. Frequency distribution and graphical representation summarize to some extent.  They reduce a mass of data to a more understandable form but not to a single value. The aim of this lesson is to determine descriptive measures or statistical constants which will describe the nature of the data.

Measures of central tendency are also known as averages. Averages are defined as statistical constants which enable us to understand in a single effort, the significance of the whole i.e., they are the representative value of the distribution. They give an idea about the concentration of the values in the central part of the distribution.

Five Types of Averages

Arithmetic Mean

It is the sum of all the observations divided by the number of observation.

For individual data or simple series (i.e., series in which all values have single frequency)

The central tendency measure is defined as the number used to represent the center or middle of a set of data values. The three commonly used measures of central tendency are the mean, median, and mode.

Measures of location (averages)

The term average refers to any one of several measures of the central tendency of a data set.

• The mean has the disadvantage that its value is influenced by outliers. An outlier is an observation whose value is highly inconsistent with the main body of the data. An outlier with an excessively large value will tend to increase the mean unduly, whilst a particularly small value will decrease it.

• The mean is an appropriate measure of central tendency if the distribution of the data is symmetrical.

The mean will be ‘pulled’ to the right (increased in value) if the distribution is skewed to the right, and ‘pulled’ to the left (decreased in value) if the distribution is skewed to the left.

One of the most important aspects of describing distribution is the central value around which the observations are distributed. A statistical measure used for representing the centre of central value of a set of observations is known as “Measure of Central Tendency”. This central value is also called as ‘Average’. The commonly used measures of central tendency are as follows;

Literal meaning of dispersion is scatterdness. We study dispersion to have an idea about the homogeneity and heterogeneity of the distribution. Dispersion gives an idea about how much the values of the observation varies from their averages. The series in which the values of the observation differ much from their averages is said to be heterogeneous or highly dispersed. The series in which the value of the observation does not differ much from their averages is said to be homogenous or less dispersed.

There are two types of measures of dispersion:

4.1 Introduction and Measuring

A measure of central tendency exhibits only one of the important characteristics of distribution, namely they typical representative figure to the whole set of its values. This measure alone will not adequately describe a set of observation unless all the observations are alike. Moreover one cannot understand completely about the data set with a measure of central tendency.  Because in real practical situation there may exits a number of sets of observations (or different distributions) whose measures of central tendency are same but they may differ individually from each other in a number of ways.  In particular two sets of values have the same mean but whilst one set of data is grouped close to the mean the other one is more spread out.  The following examples will illustrate this view point clearly.