Overview

Measurements are required to obtain quantitative information about the atmosphere. Elements of a good measurement system, one that produces high-quality information, are briefly described in the following sections. All of these items are, or should be, of concern to everyone who uses data. None may be safely delegated, in their entirety, to those who have little or no interest in the ultimate use of the data. An instrument is a device containing at least a sensor, a signal conditioning device, and a data display. In addition, the instrument may contain an analog-to-digital converter, data transmission and data storage devices, a microprocessor, and a data display. The sensor is one of the essential elements because it interacts with the variable to be measured (the measurand), and generates an output signal proportional to that variable. At the other end of this chain, a data display is also essential, for the instrument must deliver data to the user. To understand a sensor, one must explore the physics of the sensor and of sensor interaction with the measurand. There is a wide variety of sensors available for measuring pressure, temperature, humidity, and so on, and this text discusses each individually. Therefore, each chapter must deal with many different physical principles. Sensor performance can be described by reference to a standardized set of performance definitions. These characteristics are used by manufacturers to describe instruments and as purchase specifications by buyers. Static characteristics are those obtained when the sensor input and output are static (i.e., not changing in time). Static sensitivity is an example of a static characteristic and is particularly useful in sensor analysis. When raw sensor output is plotted as a function of the input, the slope of this curve is called the static sensitivity. Relating static sensitivity to fundamental physical parameters is a systematic way of revealing sensor physics and leads to an understanding of the sensor and of how to improve the design. Dynamic characteristics are a way of defining a sensor response to a changing input. The most widely known dynamic performance parameter is the time constant, discussed in chap. 6.

Sampling and Analog-to-Digital Conversion

Along the signal path from the atmosphere, through the sensors and the data logger to the final archive, the signal quality may be irreversibly comprised. These faults include aliasing caused by poor sampling practice and quantization in an analog to- digital converter. Aliasing and quantization will be defined in this chapter. Drift in some of the system parameters, such as temperature sensitivity, is generally preventable but is not always reversible. Sampling of a signal occurs in the time domain and, frequently, in the space domain with one, two, or three dimensions. In the time domain, the time interval between successive points is called the sampling interval and the data logger controls this interval. When two or more sensors are distributed, vertically, along a mast then the system is sampling both in the time domain and in the space domain. When multiple measurements are arrayed along the surface of the earth, the sampling is occurring in time and in two or three space dimensions. Most meteorological systems are undersampled both in time and space. Space undersampling is an economic necessity. The consequence of undersampling is that frequencies above a certain limit, called the Nyquist frequency, will appear at lower frequencies and this is an irreversible effect. Quantization occurs when the signal is converted from analog to digital in the analog-to-digital converter. Since the range of the converter is expressed in a finite number of digital states, signal amplitudes smaller than this quantity will be lost. This is another irreversible effect. These are not the only irreversible effects. For example, drift is caused by physical changes in a sensor or other component of the measurement system. Drift may have a causal component, such as undocumented temperature sensitivity, and a random component such as wearing of an anemometer bearing. The former is theoretically preventable and reversible, whereas the latter is irreversible. Each element of the system may include some signal averaging, and each element may add bias and gain. As noted in earlier chapters, a sensor is a transducer, a device that changes energy from one form to another.

Visibility and Cloud Height

Visibility measurement is the most human-oriented measurement discussed because the objective of such measurement is to determine the distance at which humans (pilots, seamen, etc.) can see objects. Thus we are concerned with light that can be seen by humans (0.4 to 0.7μm), the way human eyes perceive such light, and then with the transparency of the atmosphere. Throughout this chapter, in the discussion of atmospheric transparency or absorption, the range of wavelengths from 0.4 (violet) to 0.7μm (red light) will be assumed. Cloud height is a remote sensing measurement but is included here because airport meteorological systems usually include a cloud height sensor. According to the WMO, meteorological visibility by day is defined as the greatest distance that a black object of suitable dimensions, situated near the ground, can be seen and recognized when observed against a background of fog, sky, etc. Visibility at night is defined as the greatest distance at which lights of moderate intensity can be seen and identified.

Solar and Earth Radiation

This chapter is concerned with the measurement of solar radiation that reaches the earth’s surface and with the measurement of earth radiation, the long wave band of radiation emitted by the earth. The unit of radiation used in this chapter is the Wm-2. Table 10-1 lists some conversion factors. Radiant flux is the amount of radiation coming from a source per unit time in W. Radiant intensity is the radiant flux leaving a point on the source, per unit solid angle of space surrounding the point, in W sr-1 (sr is a steradian, a solid angle unit). Radiance is the radiant flux emitted by a unit area of a source or scattered by a unit area of a surface in Wm-2 sr-1. Irradiance is the radiant flux incident on a receiving surface from all directions, per unit area of surface, in Wm-2. Absorptance, reflectance, and transmittance are the fractions of the incident flux that are absorbed, reflected, or transmitted by a medium. Global solar radiation is the solar irradiance received on a horizontal surface, Wm-2. This is the sum of the direct solar beam plus the diffuse component of skylight, and is the physical quantity measured by a pyranometer. Direct solar radiation is the radiation emitted from the solid angle of the sun’s disc, received on a surface perpendicular to the axis of this cone, comprising mainly unscattered and unreflected solar radiation in Wm-2. At the top of the atmosphere this is usually taken to be 1367 W m-2 ± 3% due to changes in the earth orbit and due to sunspots. The direct beam is attenuated by absorption and scattering in the atmosphere. The direct solar radiation at the earth’s surface is the physical quantity measured by a pyrheliometer. Diffuse solar radiation (sky radiation) is the downward scattered and reflected radiation coming from the whole hemisphere, with the exception of the solid angle subtended by the sun’s disc in Wm-2. Diffuse radiation can be measured by a pyranometer mounted in a shadow band, or it can be calculated using global solar radiation and direct solar radiation.

Upper Air Measurements

Measurements of atmospheric properties become progressively more difficult with altitude above the surface of the earth, and even surface measurements are difficult over the oceans. First balloons, then airplanes and rockets, were used to carry instruments aloft to make in-situ measurements. Now remote sensors, both ground-based and satellite-borne, are used to monitor the atmosphere. In this context, upper air means all of the troposphere above the first hundred meters or so and, in some cases, the stratosphere. There are many uncertainties associated with remote sensing, so there is a demand for in-situ sensors to verify remote measurements. In addition, the balloon- borne instrument package is relatively inexpensive. However, it should be noted that cost is a matter of perspective; a satellite with its instrumentation, ground station, etc. may be cost-effective when the mission is to make measurements all over the world with good space and time resolution, as synoptic meteorology demands. Upper air measurements of pressure, temperature, water vapor, and winds can be made using in-situ instrument packages (carried aloft by balloons, rockets, or airplanes) and by remote sensors. Remote sensors can be classified as active (energy emitters like radar or lidar) or passive (receiving only, like microwave radiometers), and by whether they “look” up from the ground or down from a satellite. Remote sensors are surveyed briefly before discussing in-situ instruments. Profiles of temperature, humidity, density, etc. can be estimated from satellites using multiple narrow-band radiometers. These are passive sensors that measure longwave radiation upwelling from the atmosphere. For example, temperature profiles can be estimated from satellites by measuring infrared radiation emitted by CO2 (bands around 5000 μm) and O2 (bands around 3.4μm and 15μm) in the atmosphere. Winds can be estimated from cloud movements or by using the Doppler frequency shift due to some component of the atmosphere being carried along with the wind. An active sensor (radar) is used to estimate precipitation and, if it is a Doppler radar, determine winds. The great advantage of satellite-borne instruments is that they can cover the whole earth with excellent spatial resolution.

Precipitation Rate

Accurate rainfall measurements are required, usually over broad areas because of the natural variability of rain. Coverage of a large area can be achieved using many distributed point measurement instruments or a remote sensor with large areal coverage, such as radar, or both. This chapter describes several methods for measuring precipitation, both liquid and frozen types. Point measurements, e.g., rain gauges, are emphasized although a section on weather radar is included because this is a very important method of estimating precipitation. Precipitation rate could be specified as the mass flow rate of liquid or solid water across a horizontal plane per unit time: Mw in kg m-2 s-1. Water density is a function of temperature but that can be ignored in this context; then the volume flow rate, or precipitation rate, becomes R = Mw/pw in m s-1 or, more conveniently, in units of mm hr-1 or mm day-1. Precipitation rate is the depth to which a flat horizontal surface would have been covered per unit time if no water were lost by run-off, evaporation, or percolation. Precipitation rate is the quantity used in all applications but, in many cases, the unit of time is not specified, being understood for the application, commonly per day or per storm period. Some gauges measure precipitation, rain, snow and other frozen particles, while others measure only rain. Rainfall can be measured using point measurement techniques which involve measuring a collected sample of rain or measuring some property of the falling rain such as its optical effects. The other general technique is to use remote sensing, usually radar, to estimate rainfall over a large area. Both ground-based and space-based radars are used for rain measurement. A precipitation gage (US) or gauge (elsewhere) could be a simple open container on the ground to collect rain, snow, and hail. However, this is not a practical method for estimating the amount of precipitation because of the need to avoid wind effects, enhance accuracy and resolution, and make a measurement representative of a large area. These issues will be discussed in sect. 9.2.1.6.

Dynamic Performance Characteristics, Part 2

The first-order model discussed in chap. 6 is inadequate when there is more than one energy storage reservoir in the system to be modeled. If the sensor is linear it can be modeled with a higher-order dynamic performance model. Here the term ‘system’ refers to a physical device such as a sensor while the equation refers to the corresponding mathematical model. There exists a dual set of terms corresponding to consideration of the physical system or of the mathematical model. For example, an are coefficients of the mathematical model (see eqn. 8.1) but they also represent some physical aspect of the sensor being modeled; thus they can also be called system parameters. The general dynamic performance model is the linear ordinary differential equation where t = time, the independent variable, x = the dependent variable, an = equation coefficients or system parameters, and xi(t) = input or forcing function. This equation is ordinary because there is only one independent variable. It is linear because the dependent variable and its derivatives occur to the first degree only. This excludes powers, products, and functions such as sin(x). If the system parameters an are constant, the system is time invariant.

Anemometry

The function of an anemometer (sometimes with a wind vane) is to measure some or all components of the wind velocity vector. It is common to express the wind as a two-dimensional horizontal vector since the vertical component of the wind speed is usually small near the earth’s surface. In some cases, the vertical component is important and then we think of the wind vector as being three-dimensional. The vector can be written as orthogonal components (u, v, and sometimes w] where each component is the wind speed component blowing in the North, East, or vertically up direction. Alternatively, the vector can be written as a speed and a direction. In the horizontal case, the wind direction is the direction from which the wind is blowing measured in degrees clockwise from North. The wind vector can be expressed in three dimensions as the speed, direction in the horizontal plane as above, and the elevation angle. Standard units for wind speed (a scalar component of the velocity) are m s-1 and knots (nautical miles per hour). Some conversion factors are shown in table 7-1. Wind velocity is turbulent; that is, it is subject to variations in speed, direction, and period. The wind vector can be described in terms of mean flow and gustiness or variation about the mean. The WMO standard defines the mean as the average over 10 minutes. The ideal wind-measuring instrument would respond to the slightest breeze yet be rugged enough to withstand hurricane-force winds, respond to rapidly changing turbulent fluctuations, have a linear output, and exhibit simple dynamic performance characteristics. It is difficult to build sensors that will continue to respond to wind speeds as they approach zero or will survive as wind speeds become very large. Thus a variety of wind sensor designs and, even within a design type, a spectrum of implementations have evolved to meet our needs.

Dynamic Performance Characteristics, Part 1

When the input to a sensor is changing rapidly, we observe performance characteristics that are due to the change in input and are not related to static performance characteristics. In this chapter we will assume that a static calibration has been applied so that we can consider dynamic performance independently of static characteristics. The terms “linear” and “nonlinear” have been used in chap. 3 in the static sense. Now they are being used in the dynamic sense where “linear” connotes the applicability of the superposition property. A given sensor could be nonlinear in the static sense (e.g., a PRT is nonlinear in that is static sensitivity is not constant over the range) but could be linear in the dynamic sense (modeled by a linear differential equation). We use differential equations to model this dynamic performance while realizing the models can never be exact. If the dynamic behavior of physical systems can be described by linear differential equations with constant coefficients, the analysis is relatively easy because the solutions are well known. Such equations are always approximations to the actual performance of physical systems that are often nonlinear, vary with time, and have distributed parameters. The justification for the use of simple, readily solved models must be the quality of the fit of the solution to the actual system output and the usefulness of the resulting analysis. Dynamic performance characteristics define the way instruments react to measurand fluctuations. When a temperature sensor is mounted on an airplane these characteristics will indicate what the sensor “sees.” If the airplane flies through a cloud with a slow sensor (where time constant is large) it may not register change of temperature or humidity. That would not be tolerable if we wanted to measure the cloud. Similarly, if the airplane flies through turbulence we would like to measure changes in air speed. Variations in temperature and humidity would be vital in the flight of a radiosonde, so again the time constant of the sensors would be considered. Fluxes of heat, water vapor, and momentum near the ground require fast sensors (with small time constants).

Hygrometry

The objective of atmospheric humidity measurements is to determine the amount of water vapor present in the atmosphere by weight, by volume, by partial pressure, or by a fraction (percentage) of the saturation (equilibrium) vapor pressure with respect to a plane surface of pure water. The measurement of atmospheric humidity in the field has been and continues to be troublesome. It is especially difficult for automatic weather stations where low cost, low power consumption, and reliability are common constraints. Pure water vapor in equilibrium with a plane surface of pure water exerts a pressure designated e's. This pressure is a function of the temperature of the vapor and liquid phases and can be obtained by integration of the Clausius-Clapeyron equation, assuming linear dependence of the latent heat of vaporization on temperature, L = L0(1+∝ (T-T0)], where T0 = 273.15K, L0 = 2.5008 x 106Jkg-1, the latent heat of water vapor at T0, Rv = 461.51Jkg-1K-1, the gas constant for water vapor, e's0 = 611.21 Pa, the equilibrium water vapor pressure at T = T0, and ∝ = - 9.477 x 10-4 K-1 = average rate of change coefficient for the latent heat of water vapor with respect to temperature. Since water vapor is not a perfect gas, the above equation is not an exact fit. The vapor pressure as a function of temperature has been determined by numerous experiments.