Chapter 10

Hydrological Data

10.1 Data organization

To understand processes that intervene in the water cycle and to study their spatial and temporal variations, a database is essential. Field observations are very important for climatic statistics, for planning and management of water resources.

Measurements are recorded using a wide range of methods, from the simple writing of a number by a single observer to the invisible marking of electronic impulses on a magnetic tape. Although the most advanced techniques are used in developed countries, many nations of the third world employ only direct manual methods [Shaw, 1988].

Data Archives and Publication

Old meteorological measurements were tabulated on specially designed forms and are stored in boxes occupying considerable shelf space at headquarters. These are historical data valuable for students or hydrologists who study past extreme rainfalls. Instead of abstracting the figures manually the potential user must be able to define precisely his requirements from a system embodied in a computer software. Nowadays computer programs are written to abstract information.

Considerable attention is now given to the present need for data. The technique used to solve problems in ungauged catchments, by using information from neighbouring catchments, continues to be investigated [Shaw, 1988]. Although data publication is highly desirable, the time taken for a yearbook to appear means that data are only of historic value, useful for assessing past conditions. Operationally hydrometric data are disseminated to users for the customer's own analysis. The USA has an excellent record of data publication; its series of Water Supply Papers being well known at international levels.

The Hydrological and Geological National Service publishes the Switzerland Hydrologic yearbooks. The Natural Environment Research Council of U.K. publishes yearbooks entitled Hydrological Data. The yearbooks regroup the following results:

• daily rainfall depth;
• monthly rainfall depth;
• annual rainfall depth;
• annual average rainfall;
• average number of rainy days and variability of rainy days;
• ratio between the monthly considered module and the annual module
• maps of monthly and annual rainfall

Some of these values can be presented in an isohyets map.

The measurement results can be written as a random variable:

(10.1)

For a random variable the following characteristics can be calculated [Musy, 2001]:

- median value

(10.2)

- average value

(10.3)

- average deviation

(10.4)

- dispersion

(10.5)

- square average deviation

(10.6)

- impulses of superior order

(10.7)

- coefficient of variations

(10.8)

- centred impulses

(10.9)

- coefficient of asymmetry

(10.10)

10.2 Data control

10.2.1 Rainfall data quality control

The data are received in specialized offices by:

• postcards from observers (monthly)
• tapes from Water Authorities
• computer copying from other data set: climatic network returns

The value of rainfall data depends on the instrument, its installation, its site characteristics, and its operation by an observer. Before publishing the data it is necessary to verify missing values, correct errors, etc. This can be done starting from the original documents (filed formularies, diagrams - which constitute archives) that are accessible only to specialized personnel.

Archives are then transformed into working files to allow data visualization and verification of the data precision and quality tests. The files are then operational and can be published and distributed to users [Musy, 2001]. The hydrometric data gathering agencies are national or local government authorities, and it is their duty to publish the data and make them available to the public.

To check the daily rainfall at a station neighbouring stations data will be used through interpolation. Suspect values are discarded and then each of the daily totals is converted to a percentage of the relevant station's annual average rainfall and the interpolated percentage rainfall (R) for the testing station is given by the following relation [Shaw, 1988]:

(10.11)

The estimated value from the interpolated percentage will then be compared with the recorded value. The difference (DIFF) is considered insignificant and the record acceptable if DIFF < or = 2.5 mm and DIFF < or = 2 x error in estimation.

This checking procedure corrects automatically:

• Wrong days;
• Indicated accumulations with a simple proportioning routine to allocate the measured total among the rain days;
• Unindicated accumulations that require a searching procedure before applying the apportioning routine;
• Transposed values;
• Erroneous daily totals due to incorrect time of observation.

10.2.2 Quality control of river flow data

For each river flow station the expected response of the catchment to rainfall inputs depends on the catchment's characteristics that can be assessed, and thus a limit to the difference between consecutive stage readings can be fixed.

The daily mean discharge (m³s^-1), representing the flow volumes in a day (m³) averaged over the number of seconds, is the final product of the data processing program. They should be checked every month. Discrepancies may be found when the following checking are made:

• Comparison of the daily mean discharge with stage hydrograph traces from an autographic recorder chart, which can be made with a computer.
• The correct stage-discharge relationship has been used for the data. Different relationships may be required for different periods of the year.
• The range of flows produced is within the calibration range for the gauging station.
• The discharge converted into runoff (mm) from the catchment is commensurate with the catchment rainfall and with the runoff from neighbouring catchments.

A quality-control computer routine is designed to deal with known conditions and events. It requires different structure depending on countries and climates.

10.3 Error research and measurement corrections

There are several types of errors that can occur; on a first inspection, some of these may be identified and corrected at once, some are noted and marked, and others may remain undetected. They are:

1. "In situ"

• Misreading, misplaced decimal points, copying errors and arithmetic mistakes.
• Accumulated readings over several days entered as a one-day total.
• Correct readings entered on wrong days, persistently or only occasionally.
• Inadvertent omissions of observations made but not noted.
• Occasional errors due to temporary disturbance of the gauge or its exposure.
• Systematic errors caused by gradual alteration of exposure over a long period (years) or a leaking gauge with increasing losses.

2. Statistical investigations based on specific hypotheses. Hypotheses for a statistical analysis are:

• Measurements reflect the real values - this hypothesis is not used in practice.
• Consistency of the data - there are no modifications in the internal conditions of the system during the observation period.
• Data series is stationary - the properties of the statistic law do not change in time.
• Data are homogenous - a data series is considered homogenous when:
  • it reflects two or many different events (e.g. the stream regime downstream the confluence of two subbasins with different hydrologic behaviours)
  • the event is non-stationary (e.g. climatic variations, variation of the flow regime)
• Data series is random and simple. If all observations issue from the same population and are independent of each other, the series is random and simple.
• The series must be long enough - the length of a series influences the sample errors.

Statistical tests

The following categories are of statistical tests:

1. Tests subsequent to their mathematic properties. In most cases, these tests are based on the normal law and assume the existence of a reference random variable X. The question is whether results are valid if X is not normal: if results are valid, the test is "robust". This means that the test remains almost insensitive to certain modifications of the model.

2. Tests subsequent to their object are classified in four categories:

• homogeneity tests or tests of samples comparison

If two samples are given, of n₁ and n₂ size, can it be admitted that these samples were part of the same population, but independent between them ?

Mathematically, the problem can be expressed as following: it can be observed on the first sample the realization of a random variable X₁ and the repartition function F₁(x), and on the second sample the realization of a random variable X₂ and the repartition function F₂(x).

It can be tested:

if

if

• conformity test

The comparison of a sample characteristic values with a reference value means verifying whether the characteristic can be admitted equally to the reference value. For example H₀ : μ = μ₀ where μ₀ is the reference value, and μ is the unknown value.

• adjustment test

Verifies whether a given sample is part of a certain population.

• autocorrelation test

Verifies whether a bond exists between the chronological data of an observation series. Anderson has studied the distribution of the autocorrelation coefficient for a normal population. In this case, the autocorrelation coefficient can be calculated for n-values pairs (x₁, x₂), (x₂, x₃), …, (x_n-1, x_n), and (x_n, x₁). For a series n, Anderson limited the values at 75. The autocorrelation coefficient, after a normal law will be [Musy, 2001]:

After Anderson, Wald and Wolhowitz developed a non-parameters test of the autocorrelation coefficient, calculated by means of the following relation:

(10.13)

(10.15)

with:

(10.16)

Autocorrelation discrepancies kρ_k of a stationary temporal series is defined by:

(10.17)

Autocovariance is estimated through a n observation series x₁, x₂, ..., x_n:

(10.18)

3. Tests subsequent to the nature of information. In hydrology there are different situations depending on particular hydrological situations. Sometimes it is necessary to control just one type of data (rainfall, temperature, and evaporation) for local flow or regional flow, and sometimes it is necessary to control different types of data (rainfall-discharge, temperature-wind velocity) for local and regional flow. (More details can be found in Musy, "e-drology", 2001)

Bibliography

Musy, A. 1998. Hydrologie appliquée, Cours polycopié d'hydrologie générale, Lausanne, Suisse.

Musy, A. 2001. e-drologie. Ecole Polytechnique Fédérale, Lausanne, Suisse.

Shaw, E. M. 1984. Hydrology in practice, Second edition. T.J. Press Ltd., Cornwall, United Kingdom.

Vladimirescu, I. 1978. Hidrologie. Ed. Didactica si Pedagogica, Bucuresti, Romania.