Sustainable Runoff for Basin Salt Balance

sustainable runoff for basin salt balance, runoff quantity, sustainable irrigation, exorheic basins, endorheic basins, semi-exorheic basins, semi-endorheic basins, evaporation basin, Tulare Lake, Victor Miguel Ponce

Drain at Penoche irrigation district, San Joaquin valley, California

Fig. 1   Drain at Penoche irrigation district, San Joaquin valley, California.


Victor M. Ponce

Professor of Civil and Environmental Engineering

San Diego State University

San Diego, California


ABSTRACT:   The minimum amount of runoff that must be preserved in order to maintain basin salt balance is conceptually calculated. The alternative, the conversion of all runoff into evapotranspiration, is unsustainable, because it will cause salts to accumulate without limit. Nature intended exorheic drainage basins to be in salt balance by means of runoff. Therefore, to preserve this natural function, a limit must be imposed on the consumptive use of runoff through irrigation.


Over a measurable period, say one year, the amount of precipitation over a basin is divided into evaporation, evapotranspiration, and runoff. Evaporation (E) is the fraction of precipitation returned to the atmosphere in the absence of vegetation. Evapotranspiration (ET) is the fraction of precipitation returned to the atmosphere through vegetation. In order to avoid confusion, the combined amount of evaporation and evapotranspiration is referred herein as vaporization (V). Runoff (Q) is the fraction of precipitation returned to the ocean as streamflow.

On a global average basis, vaporization is about two-thirds of precipitation, with runoff constituting the remaining one-third. Therefore, the global average ratio of vaporization to runoff is: V/Q = 2. However, in humid regions, this ratio may be as low as 1, while in arid regions, it may be as high as 50.


In a pristine natural environment, the total volume of annual runoff is:

Ro = Qo A (1)

in which Ro = pristine annual runoff, in m3; Qo = pristine annual runoff, in m; and A = basin drainage area, in m2.

In nature, runoff always carries a certain amount of dissolved solids, mostly salts. The salt concentration in runoff is expressed in gr/m3. Thus, the total weight of salt in annual runoff is:

So = Co Ro (2)

in which So = annual amount of salt delivered to the ocean by pristine runoff, in gr; and Co = mean salt concentration in pristine runoff, in gr/m3.


Hydrologic basins can be either exorheic or endorheic, depending on their drainage properties. Exorheic basins have an outlet to the sea; endorheic basins do not. Exorheic basins have finite V/Q ratios, with a global average of 2. Conversely, in an endorheic basin, runoff is zero; therefore, V/Q = ∞; i.e., all precipitation is converted to vaporization.

Typically, exorheic basins feature rivers and estuaries, and drain outwards, while endorheic basins feature lakes and wetlands and drain inwards. However, some apparently closed basins (lakes) may not be fully endorheic, featuring small percentages of runoff, for instance, Lake Titicaca, in Peru. Therefore, these basins are termed semi-endorheic. Similarly, some apparently open basins (rivers) may not be fully exorheic, featuring small percentages of forced loss to vaporization (through small lakes), for instance, the saline bogs in the Upper Paraguay river, in Mato Grosso, Brazil. Therefore, these basins are termed semi-exorheic.

Fully exorheic drainages do not accumulate salts and other solids. Semi-exorheic and semi-endorheic drainages accumulate small quantities of salt. Fully endorheic drainages accumulate great quantities of salt.


Irrigation increases evapotranspiration. This increase can come from a reduction in evaporation or a reduction in runoff. In practice, however, for the most part, irrigation converts runoff into evapotranspiration, resulting in a net reduction in runoff. By increasing V and reducing Q, irrigation increases the ratio V/Q.

Under normal contemporary settings, irrigation reduces annual runoff to Qa, in which Qa = anthropogenic annual runoff, in m. Therefore:

Ra = Qa A (3)

in which Ra = anthropogenic annual runoff, in m3.

In addition to a reduction in runoff from Qo to Qa, the amount of salt in runoff may increase from So to Sa, in which Sa is the annual amount of salt delivered to the ocean by antropogenic runoff, in gr. The ratio

K = (Sa - So) / So (4)

is an indication of the extent of irrigation development in the basin and of the measure to which there is effective drainage of irrigation return flows. With K = 0, there is no additional export of salts from the basin; with K > 0, there is an additional export of salts. In practice, K is usually greater than zero, because irrigation development creates new salts, besides mobilizing old salts that may be already in the soil profile due to semi-endorheic drainage.


A basin is said to be in salt balance when there is no significant salt accumulation over an extended period of time, say, one year. A basin in salt balance is an exorheic basin. An endorheic or semi-endorheic basin is not in salt balance. Semi-exorheic basins may or may not be in salt balance, depending on the local drainage conditions.

For a developed exorheic basin to remain in salt balance, the mean salt concentration in anthropogenic runoff should be:

Ca = Sa / Ra (5)

in which Ca = mean salt concentration in anthropogenic runoff, in gr/m3.

With Eq. 4, it follows that

Ca = (1 + K) So / Ra (6)


Ca Ra = (1 + K) So (7)

With Eq. 2, it follows that:

Ca Ra = (1 + K) Co Ro (8)

and with Eqs. 1 and 3:

Ca Qa = (1 + K) Co Qo (9)

from which:

Qa = (1 + K) Qo / (Ca /Co) (10)

For the case of K = 0, i.e., no additional salt export, taken as a first approximation:

Qa = Qo / (Ca /Co) (11)

Equation 11 is particularly significant because it states that anthropogenic runoff is inversely related to the ratio of anthropogenic to pristine mean salt concentrations. In the limit, as Qa → 0, it follows that (Ca /Co) → ∞, i.e., salt accumulates without limit in the drainage basin, defying salt balance.

To achieve basin salt balance, Qa must remain finite; i.e., anthropogenic runoff must remain a finite fraction of pristine runoff. Furthermore, the minimum fraction to reserve for basin salt balance may be calculated by setting the ratio Ca /Co to a workable value determined by consensus of local stakeholders. For instance, if Co = 300 gr/m3, and a value of Ca = 1,500 gr/m3 is deemed to be acceptable, then the anthropogenic-to-pristine mean salt concentration ratio is:

Ca /Co = 5 (12)

and the anthropogenic-to-pristine runoff ratio is:

Qa /Qo = 0.2 (13)

When K > 0, Eq. 10 is applicable. For example, assume K = 0.1 and Ca/ Co = 5. Then,

Qa /Qo = 0.22 (14)

Furthermore, assume a high value of additional salt export ratio, K = 0.5, i.e., a highly developed basin. With Ca/ Co = 5, Eq. 10 leads to:

Qa /Qo = 0.3 (15)


An interesting and somewhat extreme case of combined natural/anthropogenic salt sequestration is represented by the Tulare Lake basin, in the southern portion of California's Central valley. Tulare Lake functions as an endorheic basin most of the time, collecting its own local and regional runoff, plus the eventual seasonal overflow from the Kings river, located to the north. However, during extreme periods of local and regional runoff, runoff from Tulare Lake was known to reverse direction and flow northward towards the Kings and San Joaquin river valleys (Fig. 1). Thus, historically, Tulare Lake has functioned as a semi-endorheic basin, with occasional drainage to the north.

Tulare Lake basin, California, c. 1874

Fig. 2   Tulare Lake basin, California, c. 1874.

Over the past century, irrigation development in Tulare Lake and environs has resulted in the conversion of all runoff into vaporization. While the intention (of irrigation) is to convert runoff into evapotranspiration, a significant portion of runoff is actually converted into evaporation (from water-supply ponds and evaporation basins). Every drop of water that precipitates in the basin is now captured in Tulare Lake basin; therefore, not a single iota of salt is being allowed to leave the basin. For the time being, the irrigation system works because the drainage system carries the salt brine away from the root zone, handles it and accumulates it in evaporation basins (Fig. 3). As the system continues to operate, the need for additional evaporation basins becomes apparent. However, it is clear that the system is unsustainable, carrying with it the certainty of its eventual demise.


The conceptual analysis formulated herein demonstrates that a minimum anthropogenic-to-pristine runoff ratio must be preserved in irrigation development if a basin is to achieve some measure of salt balance. There can be no salt balance if the anthropogenic-to-pristine runoff ratio is zero, i.e., if all the pristine runoff is converted to vaporization.

There is a maximum limit to the amount of runoff that can be appropriated for consumptive uses. Disregarding this limit leads to a loss of basin salt balance, a practice which is unsustainable. Thus, regulation of basin water quantity is absolutely necessary to preserve land quality. Stated in other terms, the preservation of water quality must not be achieved at the expense of the degradation of land quality.


A = basin drainage area (m2);

Ca = mean salt concentration in anthropogenic runoff (gr/m3);

Co = mean salt concentration in pristine runoff (gr/m3);

E = evaporation (m);

ET = evapotranspiration (m);

K = ratio of excess salts due to irrigation, delivered to the oceans, to salts delivered to the ocean by pristine runoff, Eq. 4;

Q = runoff (m);

Qa = anthropogenic annual runoff (m);

Qo = pristine annual runoff (m);

Ra = anthropogenic annual runoff (m3);

Ro = pristine annual runoff, (m3);

Sa = annual amount of salt delivered to the ocean by anthropogenic runoff (gr);

So = annual amount of salt delivered to the ocean by pristine runoff (gr); and

V = vaporization, defined as the sum of evaporation and evapotranspiration (m).

Evaporation basin in Tulare Lake basin, California

Fig. 3   Evaporation basin in Tulare Lake basin, California.