Metrological support is considered for the measurement of hydrometeorological characteristics: water flow

speed, level, and discharge, as well as precipitation, river turbidity, evaporation from water, and

evaporation from land. The systematic errors in these measurements usually exceed the instrumental errors

of the means of measurement, so it is particularly important to develop and certify methods of performing

the measurements.

Observations and measurements are the basis of hydrometeorology; the performance of the hydrometeorological sta-

tion network cannot be maintained without ongoing upgrading in the metrological support to the measurement of hydrome-

teorological characteristics, and the same applies to comprehensive environmental monitoring, especially the hydrometeoro-

logical components, and research on hydrometeorological processes and advances in forecasting dangerous hydrometeoro-

logical phenomena.

That metrological support has some major features in that indirect measurements predominate in hydrology, which

are subject to considerable systematic errors, which exceed the instrumental ones. All the measurements are performed under

conditions influenced by changing external factors, and in most forms of these measurements, there are no primary standard

means of measurement. Unified and comparable measurements can then be attained only with carefully organized and sci-

entifically sound metrological support not only to the instruments but also to the methods.

The error in any result from measurements is made up of the instrumental error of the facilities used, the error in the

measurement method, and any errors in the processing algorithms and implementation by computer. Particular importance

attaches to developing and certifying methods of performing measurements, which includes evaluating and certifying all the

above forms of error. However, up till now, in Russia and other countries, there have been no documents or legally based

metrological rules for methods of determining those errors in measurements on various hydrological characteristics such as

evaporation from water or land, snow cover, river discharge, the flow of suspended or entrained drifts, precipitation, and var-

ious other characteristics. In the guidelines [1] from the World Meteorological Organization (WMO), there are recommend-

ed errors of measurement for the following: precipitation 3–7%, river discharge 5%, evaporation 2–5%, and suspensate flow

in rivers 10%, which I consider to be desirable figures but hardly attainable ones.

There is also a problem in estimating the errors in hydrometeorological characteristics averaged over certain areas,

e.g., to determine the mean depth of precipitation on a river catchment, evaporation from water or land, soil water content,

groundwater stocks, and so on, all of which are extremely important in researching the conditions in land surface waters, and

in particular for the exact evaluation of river discharge.

I now consider how these problems are handled in the State Hydrological Institute (SHI), which is the head organi-

zation of the metrological service for the area of methods and instruments for obtaining information on the state of land sur-

Measurement Techniques, Vol. 44, No. 4, 2001

METROLOGICAL SUPPORT TO MEASURING

HYDROLOGICAL CHARACTERISTICS

PHYSICOCHEMICAL MEASUREMENTS

D. A. Konovalov UDC 556.088:556.12

Translated from Izmeritel’naya Tekhnika, No. 4, pp. 61–67, April, 2001. Original article submitted August 2, 2000.

0543-1972/01/4404-0428$25.00 ©2001 Plenum Publishing Corporation428

face waters. At the SHI,from the time of its foundation in 1919 up to the present,research has been conducted on methods

and instruments for data capture on hydrological characteristics in the environment.

Precipitation. A Tret’yakov 0–1 precipitometer is used for measuring the amount of precipitation in Russia,which

has a collecting surface of 200 cm2. A circular [2] describes the device and the method of making measurements with it,but

it contains no statement on estimating the errors in the results. The SHI experimental facilities at Valdai include the Valdai

monitoring system for measuring precipitation, which is part of the equipment in the special precipitation polygon set up in

1964 and intended for research on instruments and methods for measuring precipitation [3]. That system includes three

Tret’yakov precipitometers located in a shrub area,which protects the instruments reliably from the effects of the wind, and

where the distances between the instruments are not more than 20 m. In that polygon,close to the precipitation system,there

are Tret’yakov precipitometers in DFIR shields as accepted by the WMO as standards for mutual comparison,together with

several WNRG standard Tret’yakov precipitometers as used in the observational network as working means of measurement.

A more detailed description has been given of this polygon and precipitation system in [4,5].

Correct estimation of the errors in any form of measurement requires a primary standard at the head of a test scheme.

Until recently, no such standard certif ied in the prescribed way existed. International comparisons have been made over many

years of precipitation measurements by the Commission on Instruments and Observation Methods of the WMO, which at its

eleventh session accepted that the Valdai monitoring system (VMS) is a unique installation and provides the best estimation

of the actual amount of precipitation at the observation point,so it was decided to certify it as a primary standard. It was not

possible to estimate the errors of measurement for the VMS by the traditional method of comparison with the next standard

up in the hierarchy because there is none such, so a comparison method previously developed [6,7] was used, which involves

comparing instruments one with another and enables one to estimate errors in the absence of standard means of measurement.

However, that method gives only the random error component. Measurements with the VMS over many years [8–10] showed

that there is no systematic component in the precipitation measurement error. An additional check from those data confirmed

that the systematic component in the VMS error can be neglected.

To estimate the random error component in VMS precipitation measurement as a whole and the individual contri-

butions to it,use has been made of comparing the readings of precipitometers one with another on the assumption that the

inputs to these means of measurement are of the same magnitude. In the present case, that assumption is quite sound because

the VMS components are very close together. Then to determine the random component,it is sufficient to estimate the stan-

dard deviation σ in the results from each instrument. The random errors are taken as independent,so the mean square of the

difference between the measurements by instruments k and j when their inputs are supplied with the same quantity is

Akj = M[(Xnk – Xnj)2] = σk

2 – σj2, (1)

where Xnj denotes the measurement of quantity n (1 ≤ n ≤ N) by means of measurement j (1 ≤ j ≤ L), in which L is the total

number of means of measurement and M represents the mathematical expectation. If one estimates all the mean squares from

the (Xnj) experimental data,one gets a system of L(L – 1)/2 equations,which for L ≥ 3 can be used to determine L indepen-

dent quantities σj2:

σj2 = (Akj – Akm + Amj)/2. (2)

When one determines σj2 from (2),it is assumed that

M[(Xnk – Xavg)(Xnj – Xavg)] = 0. (3)

The random component in the VMS measurement error was determined from observations over many years on the

half-daily precipitation sums between January 1973 and December 1985. All measurements were grouped into three forms

of precipitation: solid (snow) 1705 cases,liquid (rain) 1727 cases,and mixed (snow with rain) 375 cases. Error estimates

were made for each of these. This showed that the absolute errors of the VMS in mm and the relative errors in % together

429

with the components of those errors are dependent on the amount of precipitation and can be represented by exponential func-

tions common to all forms of precipitation:

σpi = cPd; (4)

σpi = 100cPd–1, (5)

where P is the thickness of the precipitation layer derived from the three VMS components in mm,while c and d are empir-

ical parameters. We note that d is greater than 0 but less than 1,so the relative error decreases as the amount of precipitation

rises. More details are given in [4] on the methods of determining the VMS errors and the results.

This gave all the necessary evidence for certifying the VMS as a primary standard in measuring precipitation. The

State Scientific Metrological Center for Russia at the Mendeleev All-Russia Metrology Research Institute considered this

evidence and assigned the VMS the status of a standard suite for the unit of measurement of atmospheric precipitation in the

range 0.1–200.0 mm. The errors of this standard suite are given in Table 1.

This research received international recognition,and in 1998,the members of the SHI who wrote [4] were given the

highest award of WMO for instruments and measurement methods:the Wilho Weisap Prize.

430

TABLE 1. Errors of the Standard Suite for the Unit of Atmospheric Precipitation

Measurement (VMS)

Range in measured Maximum permissible relative

precipitation A, mm error σ in % at 0.95 confidence level

0.1 ≤ A ≤ 0.5 36

0.5 < A ≤ 1.0 22

1.0 < A ≤ 10.0 4

10.0 < A ≤ 200 <2

TABLE 2. Quality of Corrected Precipitation Measurements Made by the Tret’yakov Working Precipitometer by Various

Methods

Inst. Number Methods

PrecipitationNo.

of WMO RF NCcases

∆P* , % ± σ, % |∆P|/|σ| ∆P, % ± σ, % ∆ P /σ ∆P, % ± σ, % ∆ P /σ

Liquid 2 1000 –2 20 0.1 1 18 < 0.1 –4 18 0.2

7 1390 –2 19 0.1 1 17 < 0.1 –4 18 0.2

Mixed 2 270 –11/4 31/38 0.4 2 41 < 0.1 9 41 0.2

7 340 –9/5 27/36 0.3 4 38 0.1 11 39 0.3

Solid 2 1161 –7 48 0.1 –4 48 < 0.1 5 50 0.1

7 1512 –7 41 0.2 –4 48 < 0.1 4 48 0.1

* ∆P is the systematic component of the error.

When the VMS had thus been certif ied, it became possible to evaluate the performance for methods of correcting

precipitation, for which the ones examined were as follows: as developed in the RF [11],as proposed by WMO [12], and as

developed in the Nordic countries NC [13].

Table 2 compares the quality estimates of measurements corrected by those methods by comparison with the VMS

results from [14].

Table 2 shows that the results for the amount of precipitation corrected by the various methods have similar quality

parameters. The residual systematic components in the errors of the corrected measurements are much reduced, and the ran-

dom errors are also reduced, particularly for solid precipitation. For the mixed case, the systematic component of the error

remains substantial for all the methods even after correction. In the WMO method, formulas are given for correcting mea-

surements on mixed precipitation in two ways:one formula gives the correction factor for rain containing snow and the other

for snow containing rain. The formula for the snow containing rain (bottom line figures in Table 2) is more effective for the

correction,and the residual systematic component in that case is smaller, but the random component is somewhat increased.

The corrected measurements on the amounts of mixed precipitation obtained by the RF and NC methods are overestimates

and even result in changes in sign,which is clearly due to inadequate allowance for external influencing factors and the for-

mation of ground precipitation. These aspects are considered in more detail in [14].

The experimental data for that period (1973–1985) were used in estimating the errors in precipitation measurement with

Tret’yakov instruments in double shields (DFIR) and with working Tret’yakov instruments (WNRG) by comparison with the

VMS readings (Table 3). Here the errors of the DFIR and WNRG instruments are given after correction by the RF method [11].

As the VMS is in Valdai and it is impossible to set up a similar system anywhere else, the DFIR instrument can be

used as a secondary standard at any place for comparison with various types of working gauge. All our researches have been

performed at wind speeds up to 10 m/sec. At higher wind speeds,the error estimates may be different. It is necessary to con-

tinue the researches in various climatic zones in order to refine the errors for high wind speeds.

At present,the SHI has developed and certif ied a method of performing measurements on precipitation that

allows one to correct the data not only from current observations but also as accumulated in previous years for the errors

stated in Table 3.

Water Flow Speed, Level, and Discharge, River Runoff, and River Water Turbidity . Water discharge is derived

directly from the equation of continuity. Leonardo da Vinci himself considered that equal volumes of water may flow in equal

time intervals in rivers no matter what the differences in length,width, depth,and bed tilt.

A major purpose of observations on the hydrological network is to obtain reliable runoff data because runoff is a

renewable water resource form. Information on it is of the main interest to all involved with the water industry and should meet

the requirements for unification and comparability, which can be met if there is correctly organized and scientifically sound

metrological support not only to the instruments but also to the methods of measuring the runoff. SHI has conducted research

on this over many years. The runoff represents the discharge in a certain time interval (month or year),while the discharge is

determined by indirect methods such as the velocity-area one or by the use of curves relating the discharge to the water levels

at given points,so it is evident that the flow speed and level are basic hydrological characteristics to be measured.

431

TABLE 3. Precipitation Measurement Errors Obtained with Tret’yakov, DFIR, and WNRG Gauges

in Comparison with VMS Errors

Measurement Maximum permissible values of relative error in % for 0.95 fiducial probability

range A, mm WKS DFIR WNRG

0.1 ≤ A ≤ 0.5 36 80 90

0.5 < A ≤ 1.0 22 50 67

1.0 < A ≤ 10.0 4 14 26

10.0 < A ≤ 200 <2 3 8

The metrological support to means of measuring water flow speed is regulated by a standard [15], in defining which

SHI drew up a departmental test scheme [16] that established the procedure for that support in the Russian hydrometeorolo-

gy system. The test scheme is headed by the working standard for the unit of water flow speed that had been used in the SHI

since 1976. The working standard includes a hydrodynamic measuring system,which itself includes a channel of rectangu-

lar cross section with a length of 140 m,width 4 m,and depth 3 m,which is filled with water, together with test equipment

consisting of a trolley bearing a computerized data-acquisition and processing system,and rails on which the trolley moves

together with a power supply. The working standard also includes a system for checking out the sensor for the trolley speed.

In 1995–8,the working standard was upgraded. A new trolley was introduced that provided for monitoring up to eight hydro-

metric propellers simultaneously, which are fixed on four rods having electromechanical drive under remote control for up

and down displacement,together with a new computerized acquisition and processing system for the data from the propellers,

which improve the throughput and performance in checking the means of measurement. The computing section consists of a

portable personal computer based on a 486 DX2 processor with a clock frequency of 66 MHz used with the Windows 95

operating system,which provides rapid analysis of the performance of the measuring instruments for the water flow speed

during the certif ication of standard means of measurement and the checking of working ones in real time. The working stan-

dard has been certif ied by the Russian State Standard Commission as a first-class standard means of measurement for the

range 0.02–5.0 m/sec whose basic relative error is ±0.3%,and which can be used to certify second-class standard means of

measurement,which themselves are used in checking out working means of measurement in GR-19 comparator tanks.

Regulatory documents have been drawn up on certifying these standard propellers [17] and checking working ones [18,19].

The procedure for metrological support to means of measuring water level is laid down by a standard [20] and

involves a departmental test scheme drawn up at the SHI [21]. The primary standard for water level in the Russian hydrom-

eteorological service system is a primary standard equipment for checking level gauges housed at the SHI,which has been

certif ied as a first-class means of measurement and as having a maximum acceptable absolute error of ±0.34 mm in the range

0–8 m. That equipment contains a vertical steel tube of diameter 800 mm and height 10 m set up on the base of a drainage

vessel,which is filled with water that subsequently is pumped into the tube as required or drained out again through a con-

trolled valve. The change in water level in the tube simulates the input to the sensor under conditions close to the working

ones in hydrological wells. These level gauges are checked out in accordance with [22]. Before this equipment and associat-

ed instructions were introduced [21,22], working level gauges in the hydrological network in general were not checked at

all. It is too expensive to remove the means of level measurement from all the sites in Russia and ship them to the SHI for

checking, so statements of method have been formulated for checking these gauges and recording level-measuring instru-

ments directly at the point of use.

The SHI thus possesses standard means of measurement and appropriate methods for certifying and checking

meters for water flow rate and level, in order to provide unification and reliable measurement. However, it is common

knowledge that the systematic errors in determining water discharge and runoff may substantially exceed the instrumen-

tal ones,so it is particularly important to develop and certify the methods of making the measurements. SHI has intro-

duced such methods for rivers and canals based on the velocity-area method, in which hydrometric propellers are used to

measure the flow speed, as in statements of method [23],and also an industrial guideline document [24] regulating the

metrological certif ication of methods of measuring water level and discharge at hydrological stations,during which one

establishes the actual errors of measurement.

Document [23] provides for determining the overall relative error in discharge measurement as follows: 6% in the

detailed method laid down, 10% in the basic method, and 12% in the rapid abbreviated one. At low discharges,which are

related to low speeds up to about 0.4 m/sec, and also in unsteady flows, the errors may be much larger.

In another document [24],errors in measuring discharge are evaluated by summing the individual error components

as determined by a combination of calculation and experiment. An advantage of that approach is that one can research the

individual sources of error for each component in determining the discharge (errors in determining the cross section and flow

speed) in order to estimate the overall error.

These documents deal with isolated discharge measurements made not more than 2–3 times a month. Runoff

monitoring in hydrology is usually taken to imply calculated periodic or daily discharges,which are defined from the

432

correlation between the measured discharge and the water level. The task is to reproduce the runoff hydrograph as a con-

tinuous sequence of daily discharges derived from these isolated and episodic discharge measurements on the basis that

continuous observations are made only on the water levels. To transfer from the episodically measured discharges to the

calculated ones,one can use various algorithms or models,but the difficulty in drawing up a runoff estimation algorithm

is due to the variability of the riverbed carrying capacity. The simplest relationship between discharge and water level

occurs for a river having a stable bed and a steady state in the flow. If the standard deviation of the measured discharges

from the fitted relationship Q(H) is comparable with the error in measuring the discharges,then Q(H) may be said to be

single-valued, i.e., each measured water level corresponds to a certain discharge as derived graphically or analytically

from the relationship. At present,the discharge curve is usually constructed graphically: in Russia on millimeter graph

paper and in the USA on logarithmic paper [25],although it is obvious that the analytic representation of the curve is

preferable. Many researchers in Russia have examined this topic [26–28] and have found that Q = f(H) is best represented

statistically as a regression equation of the discharge on the level:

Q = a0 + a1H + a2H2 + ... + anH

n. (6)

The order of the regression equation should be determined from numerical experiments based on minimal deviation

from the approximating function. Often,the best value of n is 2–3. It remains to determine the reliability of the estimated

parameters in (6) in order to obtain an analytic formula optimally fitting the measured discharges throughout the water level

range. The following methods can be recommended:polynomial regression; weighted least-squares fitting; polynomial

regression subject to constraints in the lower part of the water level range; and piecewise-polynomial regression. The last two

methods have been adapted for fitting discharge curves in the SHI hydrometry laboratory [29]. Performance checks have been

made in numerous experiments,which have shown that polynomial regression with constraints at the lowest measured water

level provides the best fit to Q(H) for most hydrometric points.

At present,SHI is certifying algorithms and software in accordance with [30],which should resolve two basic prob-

lems:the most effective algorithms are for models for runoff accounting, which incorporate the details of various hydromet-

ric stations; and obtaining error estimates for the runoff characteristics. When these researches have been completed, guide-

lines will be prepared on estimating the errors in runoff accounting in the observational network.

Methods have been given for river water turbidity determination [31, 32], where detailed descriptions have been

given of the instruments and auxiliary equipment for water sampling and processing and for making measurements and cal-

culating the turbidity. The errors in turbidity measurement are affected by whether the bathometers with packing are proper-

ly used, where the packing regulates the water entry rate in accordance with the river flow speed, and there is also an effect

from the reliability in the turbidity measurement at a point and over a vertical section,with further effects on the reliability

in averaging the turbidity over a day, ten-day period, or month. As there are no standard means of measurement,it is very dif-

ficult to estimate even approximately what the errors are in turbidity measurement. Researches at SHI [32] indicate that the

maximum permissible relative errors for standard observations are 10–30%,while those over a day are 20–60% and are

dependent on the catchment area and observation frequency (once a day, twice a day, or many times).

Evaporation fr om Water, Soil, and Snow. Regular observations began in 1963 on evaporation in the hydrometeo-

rological station network. At that time, SHI had developed standardized observation methods and instruments:the GGI-3000

evaporation gauge for observations on evaporation from water surfaces,the GGI-500-50 and GGI-500-100 soil evaporation

meters,and also various forms of lysimeter together with the GGI-500-6 snow evaporation meter. Detailed descriptions have

been given of the instruments and observation methods in [33,34]. Current metrology does not allow one to measure evap-

oration by direct methods under natural conditions,so all experimental estimates on it are based on indirect measurements

and calculations based on the conservation of matter or energy (the water and heat balance methods),or else on the laws of

vertical transport for water vapor in the atmosphere. There are many papers such as [35–39] on estimating the errors in deter-

mining evaporation, but the lack of standard means of measurement substantially hinders obtaining reliable estimates.

Existing experimental methods of determining evaporation from land (evaporators and heat balance) enable one to determine

the monthly sums with errors close to the natural variations. It is found [35,39] that the variations in the monthly sums of

433

evaporation in the woodland zone are 15–28%,while in the wooded steppe zone they are 16–50%,in the steppe zone

27–50%,and in the desert and semidesert zone 25–70%,while the random errors in determining the evaporation with the

GGI-500 evaporator are estimated as 16–23%,while those from the heat balance method are estimated as from 15% in the

woodland zone to 50% in the desert zone, with systematic errors up to 50%.

In that connection,the SHI has developed a method of determining the systematic errors, which is based on using

evaporation formulas for land applicable to several types of territory, where the dryness index is the independent variable [35].

The idea is that routine data from the two basic methods (evaporators and heat balance) are used in constructing the correla-

tions, from which one determines the range in the discrepancies between them. Then theoretical and experimental data are

used to estimate the possible systematic errors of those two methods,which are used to correct the experimental relation-

ships. This is used to minimize the range of discrepancies between the two methods,and it gives a certain standard depen-

dence of the evaporation on the dryness index, which has been confirmed by calculations on the long-time average evapora-

tion obtained by the water balance method. That standard relationship may be compared with analogous ones from evapora-

tion determined by any other method in order to estimate the systematic errors in the latter. This gives only the zonal char-

acteristic of the systematic error, but it can be used in routine determinations for averages taken over sufficiently large areas

or for the entire warm period of the year or for the year as a whole.

Similar problems occur when one estimates errors in evaporation measurement from water surfaces made with water

evaporators, in which the evaporation between observation instants is calculated from the equation for the water balance of

the evaporator such as the GGI-3000 by reference to the difference in water levels in the evaporator between the previous and

current observation times,with due allowance for any precipitation between those level measurements. The height of the

water level is measured with a measurement tube calibrated in a pair with a burette mounted on the reference tube in the evap-

orator [40]. The main factor causing a systematic error is the heat transfer between the water in the evaporator and the sur-

rounding soil. Experimental estimates have been made on how this heat transfer influences the readings of the GGI-3000

taken at various latitudes from Salekhard to Ashkhabad [41,42], which has shown that the heat flux in northern regions is

directed mainly from the water in the evaporator to the surrounding soil. The resulting reduction in the evaporation may attain

39% of the monthly sum as measured with the GGI-3000. In southern regions,the heat flux has the opposite direction. The

exaggeration of the evaporation because of the additional heat influx can attain 27%. The random components of the error

with the GGI-3000 have been determined by using three evaporators at the Valdai polygon, where their readings were com-

pared one with another by the method described in the atmospheric precipitation sections of [6,7]. Table 4 gives the permis-

sible random errors in evaporation measurement for a day under working conditions with wind speeds up to 10 m/sec and

precipitation up to 35 mm/d at the observation point for probabilities not exceeding 0.95%.

Hydr ometeorological Parameters Ar ea Average. To estimate the errors of these, a model is used for the pattern;

it can give various error estimates. The models are constructed on various assumptions,of which the homogeneous and

isotropic model is the most common.

The homogeneity means that the averages and variances are not dependent on the points of observation and are equal

at the various points. Isotropic distribution means that the correlations and structural functions for the various points are

434

TABLE 4. Random Components of the Error for GGI-3000 Meters

Evaporation Permissible relative error σ in %

E range, mm for 0.95 fiducial probability

0.1 ≤ E ≤ 0.5 54

0.5 < E ≤ 1.0 32

1.0 < E ≤ 5.0 10

5.0 < E ≤ 10.0 6

10.0 < E ≤ 15.0 4

dependent only on the distances between them. However, most hydrometeorological patterns are not homogeneous or isotrop-

ic, and consequently the model gives error estimates that are not reliable. In this connection,the SHI has developed a some-

what different approach in which such a pattern is considered as a set of locally homogeneous and isotropic fields, so the

complete observation point set is divided into groups for which homogeneity and isotropic structure apply. The overall error

evaluation for each point will be equal to the sum of the errors for each group with appropriate weights. The weight of each

group is dependent on the density of the observation points and the errors at them. For practical purposes,importance attach-

es not only to the error estimates for the various points and quantities averaged with respect to area but also the accuracy with

which the estimates are made. It is proposed to consider the metrological characteristic patterns in terms of their errors,where

the variances and means are dependent only on the errors of the measuring instruments at the observation points and on the

methods of measurement,which in most cases are known, because the observational network employs standard instruments

and measurement methods. That approach enables one to estimate the errors of meteorological characteristics derived from

models for the patterns,i.e., to estimate the model performance.

The SHI has thus developed means of metrological support to measuring water flow speed, level, and discharge as

well as precipitation and river water turbidity. Research will soon be completed on estimating the errors in evaporation from

water surfaces and in certifying algorithms for dealing with runoff for rivers with stable beds and steady-state flow. Further

research that is far from being completed is required to estimate the errors in measuring evaporation from soil or the trans-

port of drifts by rivers.

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Rectilinear Calibration Tank [in Russian].

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Methods of Checking a Rectilinear Calibration Tank [in Russian].

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435

20. GOST 8.477-82,The State System of Measurements:State Test Scheme for Means of Measuring Liquid Level [in

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Water Levels and Discharges at Hydrological Stations [in Russian].

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