2.1. GENERAL
In this chapter definitions and meanings of some of the terms used are established, and the general importance of measurement is discussed, along with its relationship to data and variables. The treatment is not intended to be a guide to statistical and probabilistic foundations for designing a program of experimental measurement, rather it is planned to provide a general background in terminology and to be a reminder of some of the important considerations in data collections.
2.1.1. Definition and Characteristics of Measurements; Dimensions and Units
Measurement is the name given to the value or amount of length, capacity, velocity, or some other property of a quantifiable, physical entity. Measurement is obtained through the act of measuring. The values of the measurement of the physical entity serve to describe it.
Measurements are expressed by the concepts of dimensions and units.
Dimensions are the names given to those singular attributes of physical entities that describe their relation to other physical entities. Examples of dimensions are the qualities of mass, length, time, temperature and electrical charge. Many of those singular attributes are recognized in applied fluid mechanics and hydrology. Some, such as temperature, are important in defining properties of the fluid, like density and viscosity. Other attributes are quite directly part of the phenomena of fluid flow. This is particularly true of mass, length and time. For example, velocity and acceleration can.be expressed as combinations of length and time, and pressure is a combination of mass,^ length and time. In fluid mechanics practice force can be expressed through the empirical relationship of Newton's First Law, force equals mass times acceleration, where acceleration is expressed dimensionally as length divided by time squared. It should be stressed that because dimensions are descriptions of the
singular attributes they cannot be reduced further, although they can be stated alternatively through essentially empirical relationships as described above...
Units are arbitrary measures of dimensions and combinations of dimensions because measure-ments are essentially artificial and arbitrary. Although the measurement is artificial and the unit is arbitrary, the properties of the physical entity-being measured is neither artificial nor arbitrary. For example, the area of a lake is a physical reality regardless of the dimen-sions and units used to describe it. The dimension of area is usually expressed as length squared. The units of area are arbitrary, however; they can be hectares, square metres., etc.' Similarly, the time interval between discharge measurements can be expressed in minutes, hours, days, etc., and although our concept of time is that it is physically real, the. unit is arbi-trary even though it may be based on an observation of a physical phenomenon (the rotation of the earth).
There are many systems of units, but the metric Systeme International (SI) and the English are probably the most widely used. The Systeme International is the only recommended one. All systems have been developed for many years and contain units that are constructed to describe measurements of combinations of dimensions. For example, discharge can be expressed in cubic metres per second, but it is a combination of the dimensions of length cubed divided by time.
The relationship of units to dimensions is valuable in conversion from one system of units to another.
2.1.2. Simple and Derived Measurements
Simple measurements are those taken of entities or the phenomena directly, for example, flow velocity or rainfall depth. Many water- resources data are records of measurements of this kind. The data representing these measurements are very important since they are the bases for a great part of the water resources information.
Derived measurements is the name given to values of variables which are computed from other measurements, but are still values representing a fundamental variable. For example, infiltration is estimated by observing rainfall and runoff, and essentially taking the differ-ence. Similarly, discharge in a stream can be determined by measuring velocity at a number of points and combining these with measurements of the area of the cross-section of flow.
2.2. ACCURACY
Accuracy is a description of the closeness of a measurement to the true value of a •
physical entity. The concepts of accuracy of data are important in any data collection effort.
In water resources data there are problems of matching the accuracy of one set of data to another. Involved in the definition of accuracy are precision of instruments and problems of systematic and casual errors. In this section the topics named above are treated in a general fashion, and some aspects peculiar to the accuracy of water resources data are discussed.
2.2.1. Precision of Instruments
Precision is the ability to discriminate between different values of the same variable.
It largely is a function of the instrument used. As an example of instrument precision, some rain gauges are precise to 0.1 mm. The capabilities of instruments used in water resources data collection are generally well known, and information on the precision of most is generally available from the manufacturer. When planning data collection networks and management
practices it is essential that consideration of the precision of the instruments be included.
Such considerations can limit the general accuracy of the data being collected, or it can affect the selection of the instruments or the method of data reduction.
2.2.2. Sources of Error
Errors lead to an erosion of the accuracy of data. The operator or the instrument can contribute to the magnitude of errors which may be casual errors or systematic errors. Casual errors are relatively small positive or negative random variations from the true value due to various sources. They are usually described in statistical terms. Systematic errors con-sistently tend to either overestimate or underestimate the measurement. For example, a staff gauge may have an erroneous reference elevation, or a current meter may have a faulty bearing, causing drag which slows down the propeller's revolution count. Some systematic errors can be corrected if the nature of the change in the data can be ascertained. Sometimes systematic errors are present in data which are used in turn for further computation, or which are reduced in some other way, and the reduced data are all that is kept in archives. In such a case the reduced data are in error, and the correction for systematic error would have to go back to the data where the error was introduced.
Errors due to the operator's.mistakes sometimes enter into data. These are random in nature and may be sometimes positive and sometimes negative. They typically occur through human error; misreading a gauge, or writing down an incorrect number. It is also possible that a malfunctioning instrument can introduce these errors. It is virtually impossible to correct such errors unless they are noticed at the -time of measurement. Since these errors generally affect only one item of data, they are not subject to correction as are systematic errors.
2.2.3. Total Accuracy
The total accuracy is a function of the combination of instrument precision, casual and systematic errors. Instrument precision can be expressed in a statistical fashion, as a unit of precision plus or minus a number. That number usually is the standard deviation, which, if a normal distribution describes the instrument's Variation in precision, means that approxi-mately 68 percent of the measurements made will be within the range. ^ Of course, the magnitude of systematic errors and mistakes cannot be expressed in a probabilistic manner, although their occurrence can be anticipated in a.statistical sense.
The aspect of matching the accuracy of water resources measurement and data gathering to their purpose is extremely important. It is essential to consider the ways in which the data are to be used, so that the accuracy of the data is appropriate to their purpose. If un-necessary accuracy is attained, the cost of acquiring data will be higher than un-necessary, and
alternative uses for the money allocated to data collection will be lost. If the accuracy of the data is insufficient, the loss of information can never be recovered in many cases, and further losses may be incurred through poor design, faulty operation or some other, similar consequence of poor information. However, since the future use of water resources data is not known, it is considered better to err by having too much accuracy rather than too little. The senior water resources practitioner should be aware of the problem of matching accuracy, and he should understand the role the practitioner plays in matching objectives and data gathering.
Generally speaking, the accuracy of measurement should be that of the precision of the instrument. Only through techniques such as replication can accuracy greater than instrument precision be attained. However, since variables measured in water resources work are nearly always time varying, space varying or both, replication of many commonly made measurements is impossible. A measurement of less precision than that of the instrument may take just as long to perform, and so it will not represent a cost saving. The problem of matching the need for accuracy in data collection to the purpose is more severe in water resources applications since the future use is often unknown, and the requirement of the level of accuracy cannot be deter-mined. In this regard, it is important for.the water resources practitioner to record his estimates of accuracy: of the data he collects so a future user can make an assessment of its importance.
2.2.4. Temporal and Spatial Variability of Water Resources Data
Most useful water resources information is highly variable in space and time. As an example, rainfall rates vary widely during a storm, as is seen from looking at a trace of a recording rain gage. Rainfall distribution varies widely spatially, too. Similar examples can be given of nearly all water resources variables. The planners and managers of a data col-lection system must be aware of this variability and take it into account. The secol-lection of locations for measurements and the sampling intervals must be carefully considered in relation to the purpose of the measurement. There are approaches to optimization of gauging networks that have been successfully applied, and offer valuable examples of the optimization technique.
The use of "benchmark" stations, which are stations that are established for acquiring long-term records, and a program to correlate short-long-term records at other nearby stations might prove to be valuable and productive, and better than an attempt to establish a very large number of long-term stations.
Experimental basins are often used to help establish the nature of hydrological regimes, so that the knowledge .of the regimes can be extended to operational use and for development of water resources generally. The data collection networks for experimental basins will be much more extensive than those networks intended to establish a general data base for water re-sources systems. Too, the experimental basins will often have special requirements that need to be met. Much like benchmark stations, special care must be taken in the selection, location and operation of the data collection system on these experimental basins. The accuracy
expected for measurements taken in experimental basins is higher than that usually attainable in field measurements.
2.3. WATER RESOURCES VARIABLES
Measurements and data collection and storage are means to obtain values of water resources variables. The variables themselves are the things of interest and importance in the analysis, design and operation of water resources systems and in the science of hydrology. The hydro-logic cycle is studied through measurements which provide data. These data in turn serve to describe the water.resources variables, and finally our understanding of the hydrologie cycle is increased by the study of the nature of the variables.
2.3.1. The Nature of Water Resources Variables
Most water resources variables can be considered state variables of a dynamic system.
State variables are called that because they describe the state of the system at any particular time. The name comes from the literature of dynamic programming. The system is usually the catchment or some part of it, and the state variables describe its conditions. Since the system is dynamic, state variables are time dependent. In hydrological systems these state variables also have a space dependency. The time and space dependency is, of course, the reason for on-going data collections of water resources variable measurement. The very nature of time and space dependency is what the hydrologist and water resources analyst wants to determine. State variables may be exemplified by precipitation, stream discharge, soil moisture and groundwater levels.
Related-to state variables are parameters, those entities that describe the catchment itself. Examples might be stream length, basin area and a trace of the watershed. While state
variables are functions of time and space, parameters are considered to be invariant in analysis. Of course some, if not all, parameters change with time when time is measured on a very long scale, and sometimes man's activities change parameters through construction (a dredging and channel straightening project) or through land use. It is useful to think of water resources data collection in this sense because it parallels the newer ways of describing
the response of catchments through numerical simulation.
One can also describe the characteristics of water resources variables in the same general way that measurements were described in Section 2.1.1., in terms of their dimensions and units.
As with the measurements, some state variables and parameters have simple dimensional des-cription, others are expressed as combinations of dimensions. Units, of course, are arbitrary and conversion from one system of units to another is a simple process.
2.3.2. Measurements and Instruments for Water Resources Variables • Instruments used to measure water resources variables are as varied as^ the variables
themselves. Some instruments are available to measure the state variables directly. In fact, the concept of the utility of a specific variable and the development of an instrument to measure it are parallel and mutually dependent. Other instruments measure variables from which the water resources variables of interest are computed. Many instruments are standard devices in engineering and science practice. Devices for measuring length, time, mass and temperature, for example are not particularly unique to the water resources field. Other instruments are unique to hydrology, hydraulics and water resources. This list would include apparatus for measuring evaporation, precipitation and soil moisture content.
New instruments and techniques are constantly being introduced for the measurement of-water resources variables. Examples are radar for measurement of precipitation, radioactive tracers for diffusion studies, ultrasound for flow, etc. One can expect these new instruments to trigger the development of new ideas about water resources variables and their management.
2.4. DATA HANDLING
Central to the problem of producing useful data for water resources planning, management and operation is the handling of the data after the measurements are taken. A program of variable measurement and data collection is not complete unless care is given to the handling and storage of the data. The quality of the data handling and storage should be at least equivalent to the quality of measurement.
2.4.1. Data Collecting, Reliability and Reduction
Data collection should be systematic, with methods of data handling standardized as is the measurement process. Data handling includes transmission, reduction, recording, storage, and recovery, and each operation should be given attention.
Transmission of data is sometimes the simple act of delivering a notebook, but it can also include electronic transmission of signals in some way. Remote rain and snow gauges have been in common use for some time, as an example, and the information that they acquire is often sent by wire. Transmission of data can also include delivery of information to a user from the storage location or archives. Sometimes that delivery can be through electronic means. The data transmitted can be in the form of printed or written tables but it can also be on magnetic tapes or punched cards.
Data reduction refers to the transformation of the values of the measurements themselves to the values to be stored; which are the variables of interest. Reduction is sometimes done by hand, but it can be done by a computer. Care must be exercised in the reduction of data', because systematic and casual errors can arise here as easily as they do in the field. The accuracy of the information after reduction should not be less than that of the data brought in for reduction. In some cases, again using rain gauges as an example, the sensor can transmit data electronically to a central computer where the measurements are transformed or reduced to the desired variable form and then stored for future use by the computer. In such instances, no intervention by man is necessary in the flow of information. . • •
Recording,, storage and recovery of data refer to the processes of creating and using a data bank. Data are stored in the data bank; those stored data are called a data base. As implied earlier, a data bank can be a computer memory device, with electronic connections to the sensors of measurements, or terminals for entering data, and with connections to users through electronic displays, printers or some other device. Data banks can be less elaborate, too, and may simply be files, decks of punched cards, magnetic tapes, or similar storage equipment.
Whatever methods of data handling are used, the same level of care in development and operation of them should be exercised as done in the collection of measurement data. The
accessibility and reliability of the results of a data collection program is as important as any other factor in water resources development.
2.4.2. Verification and Correlation of Measurements
Independent checks of the data collected in field measurements make it possible to verify their correctness. This can be done in several ways, one of which is repetition of the mea-surement in the field, sometimes with a different instrument. For some time varying measure-ments it will not be possible to replicate, of course. In some cases an additional measurement may be too costly, or otherwise impossible. Often, verification in a rough way can be achieved in the data reduction stage through comparisons. Values which are significantly different from those of previously taken measurements may be suspected of error.
Several types of correlation, consistency and statistical analyses are available as checks on the correctness of data. In some cases it may be possible to establish the correctness of the data, or rather the lack of gross errors and mistakes, by computing the correlation coeff-icients between the observed data and other data collected at the same site or at nearby sites.
Several types of correlation, consistency and statistical analyses are available as checks on the correctness of data. In some cases it may be possible to establish the correctness of the data, or rather the lack of gross errors and mistakes, by computing the correlation coeff-icients between the observed data and other data collected at the same site or at nearby sites.