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«Water Balance Methodology for indirect assessment and prediction of basin water yield under human-induced land use changes N. V. PENKOVA & I. A. ...»

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Distinctive features of evapotranspiration connected with functioning of vegetation cover exist, namely separation of E-values into transpiration and physical evaporation from surface, vadose and saturation zones. The structuring of the E-process is of special interest to vegetation science, agricultural and ecological disciplines. As a whole, botanists and plant physiologists tend to overestimate the significance of transpiration in processes of a landscape functioning, and to underestimate the physical evaporation. In most investigations, the latter is not assessed at all. On the other hand, in applied land reclamation science, in climatology and hydrology the opposite situation observed. In most climatological and hydrological models, the process of evapotranspiration tends to be considered as a mechanistic process, the intensity of which is conditioned by the intensity of radiative heat and water budgets in plants and in surrounding space. There are many mechanistic models for the plant cover, the kernels of which consist in basic mass and energy diffusion and transfer relations. But usually they are too detailed and data extensive, which hampers their applicability to practice.

One should concur with opinion that there is a gulf between researchers and practicians within modelling of natural systems. In most applied models, which are used in practical climatology, hydrology and land reclamation sciences, E is assumed proportional to the current relative water content in the root zone, between zero-value at wilting point, and some value of optimal content, between which both the largest (energy-limited) E-values, and the greatest plant productivity are observed. In the models for irrigation rates, E is calculated within the optimal diapason of soil water content W, and the influence of plant type is accounted using “crop growth stage coefficients” and “biological parameters” which change over “biological curves” (Alpatjyev, 1974; Dorenboth & Pruitt, 1975, etc.). For example, in thе SHI model (Kharchenko, 1975) the “biological parameter” β is used, the values of which vary from 0.8 to 1.2, in the phases of active growth. The relative soil saturation γ is calculated as a fraction of field capacity Wf (E = β × E0 × γ, where E0 is potential evapotranspiration). The lower optimum (Wl) is equated with about 0.65Wf. Below the latter, E is assumed to be the linear function of γ = W/Wf.

Such a relationship was first suggested by M. I. Budyko and was based on results of laboratory experiments, i.e. under the absence of precipitation. For field conditions Budyko suggested the substitution of Wf by “critical water content” W0 under and above which E is equal to E 0. The W0-values were determined from evapotranspiration data recorded by soil evaporimeters on grasslands, and generalized over natural zones for applied climatological computations (Budyko, 1971). Later on, the linear relation for evapotranspiration efficiency E/E0 = f(W/Wf) was called into question in a number of works. However, it still is considered basic in most theoretical and applied methods and techniques.

Water Balance Methodology for indirect assessment and prediction of basin water yield 79 Latterly, the main directions for process studies were forced by finding much more significant variation for “biological” parameters. SHI experimental data from irrigated fields in the Lower Don basin showed that the β-values differ by a factor of four or more from those recommended in Kharchenko’s method. For perennial herbs in the Middle Volga District, the β-values of 100-fold and more excess were found (Penkova, 1980). The main reason for the differences was the non-accounting of the structure of E (the partitioning of E into the fast physical evaporation of intercepted precipitation and the evapotranspiration from soil). It became evident that the existing models should have been extended with regard to this factor. The problem was especially topical to rain-fed agriculture in the drought-prone “granaries” of the country located in the Middle and Lower Volga and in Caucassian economic regions. Besides, the existing techniques did not allow for important factors of cropping such as agrotechnics (fertilizer, pesticides, type of irrigation system, crop varieties and productivity, etc.) that restrained their applicability, both for planning of the growing plant development and for assessment of impact of the development on water resources and water availability. For the latter, due to non-sufficient development of complex hydrological modelling, the indirect water balance methodology was

recommended which uses the differential correlation for basic WBM-components:

ΔR = ΔS + ΔE (5) The methodology presupposes determining the ΔS and ΔE-values for a variety of surfaces and water bodies within a river basin (crops, grasslands, wetlands, forests, lakes and reservoirs, etc.). It was only seen as acceptable for relatively small land use impacts, but it requires that specific methods for water balance components have to be developed, together with the methods for scaling (weighting) the results and methods for assessment of the direct withdrawals (water intake for irrigation and water-supply development in arid lands, for population and industry need, partial runoff diversions among basins, etc.) (Shiklomanov, 1986, 1989; Voskresensky, 1986; Penkova & Shiklomanov, 1996, 1998).

As distinct from the techniques which use regionalization indices based on physics and mathematics, the indices used in ecology and soil science (water available for plants, height of capillary flux, nutrient and contaminant concentrations in soil and groundwater, etc.), and the alternative approach of explicitly nesting models for different semi-natural (uncultivated vegetation) and cultural ecosystems are used within the methodology. As the elementary units, the biogeocenotic scale ecosystems are considered since at this level the management options are usually applied in practice. Within the biogeocenoses, the scale invariant processes structure is assumed with the same processes acting in their different parts. Unlike the hydrological models, where hillslope flows are then routed through the channel network, each ecosystem is assumed to be connected with the drainage network (that nonetheless has to be proved from mean ecosystem size chosen and the mean drainage density). Among others, the aspects of spatial transference of weather data, especially variability of air humidity and precipitation, and the thresholds in catchment size, are found to be of major importance. The thresholds’ determination should consist of classification of river basins for the given region according to runoff formation mechanisms: prevailence of direct surface flows or subterranean ones (inflow, baseflow), in conformity with morphogenetic and N. V. Penkova & I. A. Shiklomanov 80 geological conditions. Formal procedures for the classification, besides the comparative–descriptive analysis, are to be based on traditional regional runoff– catchment area relations, and on the information technologies. Among the latter, the digital multi-level hydrological mapping based on ordering river basins according to the Horton-Strahler model is recommended (Penkova & Kolpakova, 1997).

The restored runoff-values should be used in both techniques

Several approaches to explicitly determine the evaporation of intercepted precipitation exist (Budagovsky, 1964; Bulavko, 1971; Andreyanov, 1977; Eagleson, 1978;

Penkova, 1978, etc.). From a physical basis, the process is usually described using the


Ep = E0*exp(-αt) (6) where α is a coefficient of declining Ep over time t. Because the equation cannot be solved due to data constraints, for practical applications the simpler relations have been suggested. For example, in monthly water balance calculations Bulavko (1977)

suggests equating Ep to potentially possible monthly interception (ΣPp) calculated as:

ΣPp = Pp × N + ΣPN1.0 (7) where N is number of days with precipitation less than Pp, the maximum value of interception during each rainfall event (1.0 mm); PN1.0, sum of daily precipitation less than Pp. The technique is not used in practice due to the subjectivity of setting Pp.

In a number of works the determination of Ep is suggested on the basis of comparing daily sums of E0 and P. For example, Andreyanov (1977) suggests

calculating E for periods of several days (decade, month) as:

E = (E0 – Ep) × W/Wf + Ep (8) n1 − n 2 n2 ∑ P( E0 ) + ∑ E0 ( P ) ; n1, n2 – number of days when P E0, and days where E p = when E0 P. The latter approach is widely used in modern hydrological modelling, but it should be qualified as high speculative, in view of uncertainty of the E0 calculated using normally available weather data. The diurnal E0-values normally do not reflect its values during the Ep-process, since the latter usually proceeds rapidly. Special observations show, for example, that the average time needed for evaporation from vegetation and land surface under sprinkler irrigation is close to 1–2 hours.

Other uncertainties concerning the E0 term are connected with techniques used for its determination. There is no uniform definition for the E0-parameter. In different works the E0 is defined as the evaporation from open water surfaces or as evapotranspiration from a full plant cover, sufficiently moistened on a large scale, under current meteorological conditions. But the latter can not be determined from the normally recorded data. They need in situ measurements with high temporal resolution. The spatial resolution of data sets is of no less importance, since the E0values for moist areas of unlimited size can not be inferred from environmental conditions normally present over land (patchy areas of moist and dry surface) that Water Balance Methodology for indirect assessment and prediction of basin water yield 81 induces the increase in E0, despite a general decrease of the radiative balance. So, the E0-term for almost all cases in practice, should be considered as an index, which more or less correctly reflects the evaporative demand of the atmosphere. Other parameters of modern heat and water budget techniques for evapotranspiration also cannot be determined with certainty using the available data. For example, because of nonlinear relationships between different variables of the Penman-Monteith equation, it is not correct to average the meteorological data over a day. If the sub-models for response of vegetation resistance to environmental conditions are to be biologically realistic, the time interval should not be greater than one hour. In other cases, the resistance should be determined over the same period (Stewart, 1989).

These circumstances force the renunciation of the calculation schemes of additive type like (7) and (8), and force a search for more general approaches. Within the water balance methodology under discussion, the possibility was investigated to construct integral semi-empirical sub-models for “biological” and other parameters of the Budyko-Kharchenko combined method. The study was carried out using a state composite water balance and agrometeorological network data (100 stations) where evapotranspiration from crops and semi-natural grasslands is being measured by soil surface evaporimeters. The main idea of the approach chosen consisted in the assumption that the theory of the processes of study is known in general features, and calculation errors mainly depend on the accuracy of parameter determination. This is due to several data constraints which do not allow the application of more explicit approaches to modelling. Among the constraints one should point out the separation of the soil body from its environment and several spatial and temporal inconsistencies. In some cases, the weather gauges are not located adjacent to experimental fields (at 10 m to 10 km distance), insufficient long periods and insufficient time resolution (the calendar 10-day step) and lack of coincidence between the date of weather record and both plant growth stages and management options (fertilizer application, hay harvest, etc.) are being observed, as well as in complete sets of measurements realized (lack of groundwater table and hydrochemical data), etc. The main task was to reconcile the integrated coarse scale sub-models with the process understanding at a finer scale.


Surprizingly, the results obtained are good. They not merely confirm several theoretical ideas of the evapotranspiration process, but they have the inherent theoretical advantage over existing mechanistic approaches. As an example, several graphic relationships constructed using cubic splines are presented in Figs 1 and 2 for different natural conditions. The diagrams in Fig. 1 demonstrate that under very low yield, the increasing mineral nutrition corresponds to a considerable increase in total evaporation, for average yield (15 to 30–40 c ha-1) increasing β is characterized by saturation at different levels of Vf, and under high productivity of 60 c ha-1 and above evapotranspiration is steadily lowered with Vf which is in good agreement with existing notions about water exchange processes in rain-fed agriculture. In Fig. 2, the relationships between Cd and D-parameters, groundwater table (Hgr, m) and Cl-ion concentration in groundwater (mg L-1) are presented which are obtained using Heat N. V. Penkova & I. A. Shiklomanov 82

–  –  –

where Wb, We are productive soil water content at the beginning and end of the calculation period (mm); Cd is structural-dynamic parameter-function analogous to βparameter; D is “total error” (mm). Cd-values obtained from rearranged equation (9), and D-values that include elements of water exchange of active soil layer (Kg, Ig), measurements errors (dE, dP, dW), and non-accounted delivery of moisture (η) (precipitation intercepted by plants, dew, adsorption of moisture by plants, etc.), both are complex nonlinear functions of environment and plant physiology factors. The graphs corroborate several important features of the composite groundwater–soil– plant–atmosphere system: influence of groundwater depth on plant water intake (Cd-changes), transformation of water exchange in vadose zone (increasing of negative D-values with Hgr lowering due to deep percolation), and influence of chemical composition of shallow groundwater.

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