Integrated Design of Hydrological Networks (Proceedings of the Budapest Symposium, July 1986). IAHS Publ. no. 158,1986.

Principles of specifications of optimum networks of hydrologie observation sites

Principes sur les caractéristiques des réseaux de sites d'observation hydrologique optimaux

I.F. KARASSEFF State Hydrological Institute. 2-nd line, 23 Leningrad, 199053, USSR

ABSTRACT Quantitative criteria are formulated for the optimization of hydrologie networks to study runoff characteristics and to obtain operational and forecast data. To account for variations within a regime, correlation of statistical characteristics of fields of hydrologie elements and structures of a hydrographie network (orders of streams) are used. Criterion drainage areas for zones of thé USSR are determined which can be transferred to other regions with analogous landscape and climatic conditions. As applied to operational and forecast problems, optimum correlations for choosing basin predictors and completeness of hydrometric runoff control when calculating water balances are indicated. It is of great importance that principles of network optimization account for specific economic and geographi­cal conditions.

GENERAL CONSIDERATIONS

Networks of hydrologie observation sites are created to obtain data on the regime and state of water resources such as rivers, lakes, and reservoirs. River runoff, which determines the network structure, is the basic element to be observed. With respect to other elements, network efficiency should be tested for each case. This problem is complicated by the mixed nature of continuous and discrete spatial distributions involved in the links and nodes of river systems.

Optimization of a network consists of specifying the density of observation sites that will be sufficient for obtaining reliable data while not requiring the establishment of an excessive number of sites. Although hydrologie elements always are related to a discrete river-basin area, when considering a territory of sufficiently large dimensions, for example regions or zones, we may assume a continuous distribution of these elements.

SPECIFICATION OF A NETWORK FOR INVESTIGATING ZONAL RIVER RUNOFF CHARACTERISTICS

Within the limits of some quasi-homogeneous region, annual runoff 3

4 I.F.Karasseff

from a drainage area of sufficient zonally representative size k^ can be represented in a simplified form as a function of one coordinate:

Q(l) = "Q(l) + f(D (1)

where f(l) is the random runoff fluctuation from its norm Q(l) for an individual year. Two criteria that assist in determining the density of observation-site locations can be derived from this representation. The gradient criterion is based on the first term of equation (1) as a minimum necessary distance Çgr between centers of basins to allow the definition of the difference in runoff norm (Karasseff, 1972):

2.826 ÏÏ Sgr

> 2=r (2) grad0(Q)

where Q0 is the averaged (over the area) value of runoff norm in the given hydrological region, grad0(Q) is the mean relative gradient of the change of runoff norm within the limits of a hydrological region; and ô0 is the error of determining annual runoff from hydrometric data. The gradient criterion Çgr corresponds to drainage area Agr. Thus, the greater the distance between sites, the more reliably the change of runoff norm is determined. But a boundless increase of drainage area per station would lead to loss of annual flow correlation. To avoid this problem, it is necessary to fix the upper limit of the distance between centers of gaged basins.

This limitation creates a correlation criterion derived from the second term of equation (1) in such a way that the error of linear interpolation of annual runoff for the middle of the distance between centers of basins will not be greater than 60:

62n Cc < -f lQ (3)

C v

where Cv is the coefficient of variation of annual runoff and £0 is the correlation radius where the autocorrelation function of annual runoff becomes equal to zero (in the average for the USSR territory £,0 = 1,600 km). An area Ac corresponds to this correlation criterion.

The optimum drainage area A0 should be within the range:

Azr < Agr < A0 < Ac (4)

Values of characteristic drainage areas are determined for all hydrological zones of the Soviet Union. This also was done in Canada for the Quebec province (see table).

Principles of optimum networks 5

TABLE 1 Criterion areas for planning basic hydrological networks (km^)

Characteristic drainage areas,

in km2

USSR zones tundra forest steppe

Canada

Azr

200 500

1,500

"

Agr

-4,000 2,000 8,950

Ac

32,000 7,000 2,000 20,590

Optimum

Ao

15,000 5,000 2,000 15,600

HYDROLOGICAL NETWORKS FOR AZONAL (SMALL) AND POLYZONAL (GREAT) RIVERS

Values of A0 generally are drainage areas of midsized rivers for which zonal regularities of runoff formation are characteristic. For other rivers—small azonal with drainage areas less than Azr, large (polyzonal), for which the drainage area is greater than A0, as well as for rivers with anthropogenic changes of runoff— the principle of locating observation sites at control points is applied and depends on the structure of the river system. Accor­dingly, at least one observation site should be located on each large river and on selected small rivers for controlling their runoff and stage. River networks can be represented as tree-type graphs (Fig.l) where nodes represent sources and inner-points of watercourse confluences. Properties of the parameters of river systems are indicative of hydrologie processes. Many character­istics of river regime, such as mean water content, maximum discharge, and ice thickness, can be represented as functions of different structural measures, in particular—of the orders of river streams "K." Therefore, indices of river network structure become an additional source of hydrologie information. In the case of homogeneous climatic and orographic conditions, characteristics obtained in the region where observations have been made can be transferred to other rivers of the same order where observations do not exist.

This follows from the principles of locating observational sites (Fig.l). In general, sites should be located in all links of streams of different order, or at least on those that are of most importance for users of hydrologie information. Thus, together with traditional principles of relatively even location of sites that are applicable when establishing networks for studying zonal characteristics, a new approach of concentrating observational sites in basic links of river systems will be efficient. In any of them at least one chain of sites A - + B + C + D + E should be created, spreading over the whole graph of a hydrographie network.

According to the conditions mentioned above, a certain number of

6 I.F.Karasseff

FIG.l Graph of river system.

sites, Ns, should be established on small rivers, the order of which, Ks, is less than the order, K0, of rivers with the optimum watershed. In this case, watersheds characterized by different types of relief, forest coverage, lake percentage, number of swamps, etc., are selected from a large number of small rivers. In addition, on mountain rivers the locations of sites should take into account the regularities of runoff change with elevation. Also, with the increased usage of water resources and economic development of a territory, it becomes necessary to study individual water bodies— rivers, river reaches. In this connection, the principle of "objective" location becomes valuable first of all on rivers with drainage areas greater than the optimum A0. In this case, the definition of regime characteristics—extremum discharges, data on level fluctuations, water temperatures, sediment runoff, etc.—should be considered the major task. It follows that it is necessary to have at least one site on each river with order, K, higher than the optimum one, K0. The number of sites on such rivers is determined by Horton's relation:

where s is the order of a river system; and r is the bifurcation ratio forking, which on the average is equal to 3.

The total number of hydrological sites will equal:

Principles of optimum networks 7

M = Ms + N0 + Ni » (N0 + Ni)(l + a) (6)

where a is the portion of sites on small rivers (usually is taken equal to: a = 0.15 - 0.30), and N0 is the number of sites in the network for defining zonal characteristics.

OPERATIONAL FORECAST NETWORK

Under modern conditions, the role of water as a factor in the economy and social development of society has grown considerably. Earlier hydrology was limited to studying regimes of water bodies and retrospective calculations of their hydrological characteristics; now current data and forecasts of water conditions as a dynamic system have become most necessary.

One of the most important objectives of an observation system is obtaining of data for forecasting. For forecasting water regime of rivers, data on discharges and levels of water in small (partial) watersheds usually are used. It is natural that when a sufficient number of small watersheds is distributed evenly over the basin, unevenness of inflow of melt and rain water, distribution of losses, and other factors can be taken into account most correctly. On the other hand, superfluous information is undesirable because it requires additional expenditure. Therefore, it is important to determine the optimum number and area, A±, of small watersheds, by which it is possible to forecast with a permissible precision the runoff of a mainstem river at the outlet of basin with an area A.

The value of a subbasin with drainage area, A-̂ , from an informa­tion viewpoint, can be estimated by the degree of correlation of runoff from this subbasin with runoff at the outlet. Special investigations have shown that coefficients of correlation of these values increase with the growth of the ratio, 3 = Aj/A. However, in the case of large 3, a correlation coefficient becomes irrelevant because the warning time of a forecast decreases toward zero. The optimum interval of relative areas for subbasins lies within the limits 30 = 0.01 - 0.02.

Locating hydrological sites in the zone of multi-purpose use of water resources gains special importance. Network structure is predetermined in this case not only by geohydrologic and morphologic conditions of the basin, but also by its subdivisions into admini­strative and water-management units (Fig.2).

Runoff observational sites should be located: (a) in the lower part of inflow and wastewater canals; (b) at the heads of irrigation and watering canals taking water

from the sources; (c) at the beginning of a debris cone before the zone of infil­

tration, and at its end, where ground-water decrement takes place; (d) at the boundaries of irrigated areas and zones of consider­

able industrial water diversions (towns); and (e) at the sites of hydroelectric power plants and hydroprojects. In the zones of runoff, water-use data serve as a part of the

information supply for automated systems of control of water-management complexes, which may be carried out both in a dynamic regime and on a water-balance basis. In particular, in the case of

8 I.F.Karasseff

/ I

V / t

Water-management-region boundary H»i—i Administrative boundary

" Water diversions

—*• Return flows — o River gages v Channel gages

FIG.2 Hydrographie scheme of water-management regions and network of stations for observations on runoff and runoff use.

water distribution, operational channel water balances (CWB) are used, which are calculated for different periods (10-day period, month, year) for separate river reaches.

The CWB equation results in the most simple form in the case of a steady regime of flow:

Qu - Qi + Qii + ^Qwi - 2 Q <!et ± Qf ± Qr = 0 (7)

where Q u is discharge at the upper mainstem site; Qi - is at the lower (outlet) site; Qi^ is lateral inflow; Q wi is water diversions into channels; Q e is removals from them; Q e t is losses for evapora­tion and transpiration; Qf is losses for filtration or inflow of infiltration water; Q r is the' residual term that compensates for elements not taken into account and errors of computation.

Composition of data for compiling a CWB depends on the pre­selected error 6 0 of its calculation. For example, according to the principle of equal effects on error A 0, the value of partial error of the determining of some element should meet the following inequality:

x-i/N (8)

where a^ is the portion of the element from the whole sum N of elements composing CWB; that is,

< / < i / I j Qi

From equation (8) it is evident that, in the case where 6^ is much larger than the coefficient of variation instead of measured values of the i element when computing the CWB, we can take its norm Q.. From this we can derive the criterion of network optimization:

Principles of optimum networks 9

within the area of applicability of a CWB, all sites should be operated so that for 6j_ is less than the coefficient of variation of the element, and the permissible error of measurement according to inequality (equation (8)) should not be exceeded. Thus, the principle of equal influences leads to not only the quantitative criterion of site locations, but also the condition of optimization of the precision of observations carried out at these sites.

Spatial-data interpretation at observation sites requires the use of modern technology with broad coverage such as aerial and satellite surveys. Information from space on snow and ice cover, river floods, the state of underlying surface, etc., is of special importance.

Nowadays in some countries mathematical models are being developed and some already are created that produce a hydrograph of runoff from watersheds with little or no classical hydrologie data. In these models, in addition to the classical data, remote-sensing data also are used. For effective coordination of ground-truth and remote-sensing observations, it is efficient to create special plots and groups of sites in different physiographic conditions. In the USSR, experience exists in which successful operation of hydrometric networks of a complex of observations on rivers in inaccessible regions of the North and Far East is carried out.

When creating a remote-sensing system, applicable properties of river systems should be used to their full extent. It follows that it is efficient to create optimum systems of test plots and sites to carry out ground-truth observations for standard decoding of remote-sensing observations.

A test system of subbasins ensures considerable expansion of the information on the regime of water bodies and creates new possibili­ties for hydrologie forecasting.

Apart from remote sensing, satellites can be used as a means of relaying information from surface-measuring sites. Such communica­tion satellites, as the U.S.A. experience shows, are perspective methods of transmitting hydrological data from remote sites to information users; they will be especially advantageous when organizing networks in inaccessible regions.

Thus, nowadays, of course, when carrying out extensive investiga­tions, it becomes possible in principle to create new systems for making forecasts of almost all types of runoff, and particularly methods of runoff calculation on the basis of remote sensing. It seems that new systems of runoff forecasting will gradually supple­ment, and in some cases, where it happens to be more precise and more economically feasible than the existing one, even substitute for the latter.

REALIZATION OF PRINCIPLES

The above scientific principles are used when making plans for development and rationalization of a hydrologie network in the USSR. The optimum number of sites of a USSR hydrologie network is 7,800 with a mean of 3,000 km2 per site, which is close to density of the hydrologie network in Canada, but is 3 to 3.5 times less than that in the U.S.A. and an order of magnitude less than density of sites

10 I.F.Karasseff

in the Western European countries. This fact demonstrates the great role of specific economic and

geographic conditions that should be taken into account when specifying optimum hydrologie networks.

REFERENCE

Karasseff, J.F. (1972) Physical and statistical methods for network design. In: Casebook on Hydrological Network Design Practice, World Meteorological Organization, WMO Publ. No. 324, paper III-l.l, 10 p.