durango, mexico

Transcription

durango, mexico
MODELLING THE WATER BALANCE COMPONENTS FOR
THE MANAGEMENT OF THE WATERSHED ‘LA ROSILLA’
DURANGO, MEXICO
Modelación De Los Componentes Del Balance Hidrológico De La Cuenca ‘La Rosilla’
Durango, México
José Návar1
Professor of Natural Resource Management, CIIDIR-IPN, Unidad Durango. Calle Sigma s/n. Fracc.
20 de Noviembre II. 34220. Durango, Dgo., México Tel & Fax + 618 8142091.
e-mail: [email protected]
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ABSTRACT
The man-made reservoir ‘La Rosilla II’ services water
the city of El Salto, Durango, Mexico for public and industrial supply. There is uncertainty on the risk of floods during wet spells
and the lack of storage during dry episodes to meet conventional fresh blue water demands of an increasing population and
industry. In spite of this, there are no studies dealing with the understanding of the components of the hydrological cycle within
the watershed that drains into the reservoir and this research
attempts to establish the basis for modeling the hydrologic components with the aim to sustainable manage blue water resources in the watershed. Although shortcomings of this study such
as running the model with a better temporal resolution and calibrated with reservoir data, preliminary observations show that
the watershed produces sufficient annual discharge to saturate
the storage capacity of the reservoir on 68% of the time and as
consequence it is recommended to augment the storage capacity of the reservoir or to build up a second reservoir. It is also
recommended to develop a management plan for the reservoir
itself that accounts for the temporal variations of the hydrological
cycle and water demands of the population of El Salto, Durango, Mexico.
Key words: Drought and wet spells, Mass balance hydrological model, Annual discharge.
RESUMEN
La presa ‘La Rosilla II’ abastece de agua a la población
de El Salto, Durango, México para uso doméstico e industrial.
Existe incertidumbre sobre el peligro de inundaciones y falta de
agua azul en épocas de sequías para satisfacer las demandas
de una creciente población e industria. A pesar de este panorama, no existen estudios encaminados a entender los compo-
nentes del ciclo hidrológico en la microcuenca que abastece el
embalse y este trabajo de investigación intenta establecer las
bases para el modelamiento del sistema con la finalidad de manejar sustentablemente el agua en la zona. Aunque el modelo
del balance de masas necesita una mejor resolución temporal
y de calibración con los datos del embalse, observaciones preliminares indican que la microcuenca produce suficiente agua
azul anual para saturar el almacenamiento del embalse en el
68% del tiempo y como consecuencia se recomienda aumentar
la capacidad de almacenamiento de este embalse o crear otras
fuentes de almacenamiento. Así mismo se recomienda desarrollar un plan de manejo del mismo embalse que considere las
variaciones temporales en los componentes del ciclo hidrológico y de las demandas de agua en la ciudad de El Salto.
Palabras clave: Sequías y periodos húmedos, modelo hidrológico de balance de masas, descarga anual.
INTRODUCTION
Conventional management of water resources cannot meet
future water demands for development in northern Mexico.
Erratic and variable water supplies featured by hydro-climate
variations and unsustainable practices of hydrologic resources
are depleting freshwater resources for human use. The over
exploitation of aquifers, reduced recharge, a high ratio of volume of irrigation to productivity, and a high per capita water use
are some unsustainable practices (Návar, 2001; 2004; Ward,
1998; Schmandt et al., 2000). Other unsustainable practices are
high losses of water in the distribution systems of most cities
(30-40%) (CNA, 2000), contamination of streams, reservoirs,
and aquifers impairing further water use (Vogel et al., 1995;
Flores-Laureano y Návar, 2002; Lizárraga et al., 2005; 2006),
river fragmentation by the construction of reservoirs and the
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mands of an expansive irrigated agricultural area (SEMARNAT,
2004). Biological indicators of degradation of water resources
are losses of species diversity that dwell in streams (Contreras
and Lozano, 1994; Edwards and Contreras, 1997) and changes
in species structure of riparian trees, benthic insects and fishes
(Guerra-Pérez and Návar, 2008). River modification, contamination, drawdown of reservoirs, and river fragmentation partially
explain losses of wetland species in northern Mexico.
In addition to this state of affairs, potential global warming
may be also contributing to increasing the temporal and spatial
variations of water resources on most arid and semi arid lands
of northern Mexico. The region is projected to receive 10% less
rainfall and to produce between 5 to 10% less streamflow by the
end of this century if climate change models are correct (Mulholland et al., 1997; IPCC, 2001; 2007). Návar (2001) observed
that in the presence of worst drought episodes on record there
is 12% less rainfall and 27% less streamflow in the San Juan River of northeastern Mexico. Therefore, climate change may already be or may in the near future be magnifying drought spells
and reduce river flow and water supply in the region. Regardless of this state of understanding and the importance that river
discharge represents to meet conventional and holistic water
supplies, there has been little effort to understand the quantitative importance of the components of the hydrological cycle
in watersheds of northern Mexico and how these mechanisms
vary in time and space within watersheds. This information is
useful when coupled with climate change models and future
scenarios on water demands.
The main components of the hydrological cycle are
precipitation, evapotranspiration (interception loss, evaporation,
and transpiration), discharge (surface and sub surface runoff
and leakage or deep percolation into aquifers), and changes
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in soil moisture content. Spatial and temporal variations of these components are the rule in semi-arid watersheds (Ward,
1998). For example, drought spells for northern Mexico for the
last century are well documented during the periods of 18901910; 1920-1930; 1950-1964; 1990’s that are featured by precipitation and discharge consistently below the average (Návar,
2001; 2004; 2008; Návar et al., 2010). Wet periods have also
been recorded for this region during the 1940’s; the 1960’s; and
during the 1970’s-1980’s (Návar, 2001; 2004; 2008; Návar et
al., 2010). Shifts in precipitation variables tend to promote major
changes in the other hydrologic variables. However, how variation expands form precipitation to; e.g., discharge or soil moisture content has been little understood in Mexican basins.
In light of this review, this research addresses the following issues: a) the physical modeling of the components of
the water cycle, b) the sensitivity analysis of input parameters
of a hydrologic model, and c) the plan proposal for the management of water resources for the watershed ‘La Rosilla’ of Durango, Mexico.
MATERIALS AND METHODS
Location of the study area. This study was conducted at
the watershed ‘La Rosilla’ which drains into the ‘La Rosilla II’
reservoir, located at the Ejido La Victoria, Municipality of Pueblo
Nuevo, Durango, México. The city of El Salto supply most of its
domestic water from this reservoir and part of the city is placed
within the Ejido ‘La Victoria’, as well. The watershed covers an
area of 944 ha and it is geographically found at the coordinates
23° 44´ 00” north latitude and 105° 27´ 00” west longitude, at the
southwestern portion of the Sierra Madre Occidental mountain
of Durango, Mexico (Figure 1).
ESTUDIOYMANEJODELOSRECURSOSNATURALES
Figure 1. Location of the watershed ‘La Rosilla’ Durango, Mexico.
The watershed sits within the Hydrologic Region No 11 (Presidio-San Pedro), in the uplands of the Rio Presidio basin. The
main stem of the river is named Arroyo Quebrada El Salto, a
tributary of the Rio Presidio (CFE, 1998).
According to the Köppen climatic classification scheme and
modified for Mexico by García (1987), the ejido features several
types of microclimates: a) the highlands feature the temperatecold, humid climate, with summer rains and mean annual temperature between 5 to 12 °C, classified as C(E)(W2); b) the rest
of the ejido presents a temperate, humid climate with summer
rains, and mean annual temperature ranging from 12 to 18°C.
Summer rains are characterized by thunderstorms concentrated between July and September. Mean annual rainfall depth
and temperature at the climatic station of El Salto is 1,000 mm
and 9.3°C.
Most of the watershed is covered by temperate forests with
mixtures of pines and oaks. Main pine distributed species are
Pinus cooperi, P. durangensis, P. engelmannii, P. teocote, P. herrerae, P. leiophylla and P. ayacahuite. The most frequent oak
species observed are Quercus sideroxyla, Q. durifolia, Q. rugosa and Q. candicans. Juniperus spp., Cupressus spp. Pseu-
dotsuga spp and Abies spp are other conifer species that make
up isolated communities within the watershed. Other broad
leaf species are Arbutus spp and Alnus spp. The lower strata
is conspicuous and dominated by manzanita (Arctostaphylos
pungens) and encinilla (Quercus striatula).
P' G = −
RSc  Ec 
ln 1 −
Ec  R 
[2]
The hydrological model. The components of the water cycle in forested watersheds were estimated using a model based
on the mass balance budget (Návar, 2007). The model is physically based and computes changes in the soil water storage as
a function of the difference between inputs and outputs. Input
is rainfall and outputs are interception, evpotranspiration (transpiration and evaporation of water from the soil) and discharge
(surface runoff leakage to aquifers); see Equation [1]. This model assumes that the amount of soil water above field capacity
leaks down into shallow perched water tables that eventually
transforms into discharge via subsurface and aquifer discharge.
The intrinsic hypothesis is that there is little or not surface runoff,
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and it appears to be correct for most forested soils for most of
the time, since high average final infiltration rates of the order
of close to 130 mm h-1 were measured, and that only 7% of the
rains which occur annually and close to 30% in rains that have
a frequency of a two-year return period produces surface runoff
(Dueñez and Návar, 2005).
n+m
m
n
n
j=1
j=1
j=1
j=1
∑ I j = c∑ PGj + (cEc / R )∑ (PGj − P' G) + c∑ P' G + qst + pt
Rainfall, P, is conventionally recorded in gauges at the climatic station El Salto, Dgo., Mexico. Leakage or percolation,
Qs, equals to discharge, Q, since surface runoff, Qs = 0. Interception is the amount of rainfall that wets canopies and litter
(leaves, bark, and litter) and returns to the atmosphere via evaporation without contributing to soil moisture.
m
n
n
j=1
j=1
j=1
j=1
∑ I j = c∑ PGj + (cEc / R )∑ (PGj − P' G) + c∑ P' G + qst + pt
Where: Ēc = the evaporation rate during the storm per unit
area of cover, Sc = the canopy storage capacity per unit area of
cover, R = the average rainfall rate onto the canopy.
The canopy structure parameters, climatic factors, and interception components of the revised Gash model were estimated as follows. The canopy cover coefficient (c) was directly
measured in the field by measuring canopy cover of all trees in
each stand, using an optical densiometer. The canopy storage
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∑ PGj
[1]
j=1
The revised Gash et al. (1995) analytical rainfall interception loss model was used to predict interception loss since it is
simple, flexible, and requires a few parameters, which can be
easily derived. The model has been reformulated to give a better description of the evaporation flux from sparse forests. Gash
et al. (1995) introduced the following analytical model of rainfall
interception [2]
n+m
Where I is the interception loss depth, m is the number of
small storms insufficient to saturate the canopy (i.e., < P´G), n
equals the number of events which saturate the canopy (i.e.,
> P´G ) and q equals the number of storms which saturate the
trunks, PGj is gross rainfall, st is the trunk storage capacity, pt is
the proportion of rainfall reaching the trunks, P’G is amount of
rainfall necessary to fill the canopy storage capacity.
n −q
n −q
∑ PGj
[1]
j=1
capacity parameter (S) was assumed to be the intercept of the
relationship between interception loss and gross rainfall (Figure
1). Sc was calculated as S/c. The proportion of rainfall that is
stemflow, pt, and the storage capacity of branches and stems,
St, were assumed, consistent with Gash (1979) assumptions, to
be the intercept and slope of the relationship between stemflow
and gross rainfall. The mean rainfall rate on to the saturated
canopy (R mmh-1) was determined from rainfall depth measurements at the site and event duration values recorded at the
climatological station at Durango, Dgo., Mexico. The mean evaporation rate from the saturated canopy during rainfall (Ec mmh1
) was estimated by multiplying the slope of the interception loss
versus incident precipitation depth relation by R times the canopy cover coefficient. The coefficient and parameter values for
the Gash et al. (1995) revised analytical model are reported in
Table 1.
ESTUDIOYMANEJODELOSRECURSOSNATURALES
Table 1. Coefficient and parameter values for the Gash et al. (1995) revised analytical model of rainfall interception for temperate forests of northeastern Mexico (Source: Návar, 2010).
Evapotranspiration, Et, is the amount of green water that
leaves the soil via evaporation from the soil surface, Ev, and via
transpiration, Tr, as a vital process conducted by plants. An estimator of Et is measured in conventional evaporimeters; and it is
named potential evaporation, Etp, because water is fully available for climate to evaporate. Actual evapotranspiration, Et, is the
potential evapotranspiration weighted by soil moisture content
(θi), plant (Ftv), and climatic (Fc) factors. Soil factors that control
Et are the current water content, θi, the water content at wilting
point, θpmp, and the soil water content at field capacity, θcc.
The plant factor is a function of the type of vegetation, density,
age, etc. The climatic factor is a function of the climate parameters that control evapotranspiration (Net radiation, wind speed,
moisture deficit, etc.). Evapotranspiration is estimated using
these factors as in equation [3]:
θ i − θ pmp 

Ln 100 ∗
θ cc − θ pmp 

Etp =
∗ Et ∗ Fc ∗ Ftv
Ln(101)
Details of the soil, plant and climatic factors can be found in
several books on hydrology, soil physics, and climatology (Hillel,
1982; Viesmann et al., 1996). In this study, twelve soil samples
were collected and distributed within the watershed for physical
analysis to estimate the field capacity, the wilting point, soil bulk
density, and soil specific density. On site, the depth of soil and
litter layer was also measured. The coefficient and parameter
values for the soil components of sub model 3 are reported in
Table 2.
The model was run in a time difference of one day to estimate the current soil moisture content; i.e. θi = θi -1 ± [Precipitación
– Intercepción i-1 – Etp i -1]. Where: the i-1 refers as the day bei-1
fore day i. Again, discharge was estimated as the soil moisture
content that runs off and that is mathematically described as
the amount of soil moisture content above field capacity and
this amount of water is subtracted immediately to attain the soil
water content at field capacity. Since at this time there is a lack
of information on the shape and rate of recession flow, the time
of concentration, time to peak, peak flow, etc., hydrographs can
not be derived at this point with this model.
All this data was employed to run the hydrological model.
Information to develop the interception loss model of Gash was
obtained from measurements conducted on mixed, pine-oak
temperate forests of Nuevo Leon, Mexico by Návar (2010). The
climatic factor, Fc, was estimated to be 0.75 in agreement with
findings carried out by Penman (1986). The plant factor, Ftv,
was estimated to be 1.25.
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A sensitivity analysis was conducted on the hydrological
model by adding the 95% confidence interval values to the
mean input parameters. This analysis was conducted for the
interception loss parameters Ec, pt, St, and a; for the soil parameters θcc and θpmp; and for the climatic and plant cover
factors. The analysis assumed that the ratio of the confidence
interval to mean field capacity was similar to the estimate of the
confidence interval for the last two parameters (Fc and Ftv). Resulting figures of interception loss, average soil moisture con-
tent, and total annual discharge were taken into consideration
in the sensitivity analysis. All hydrological parameters (total annual interception loss, evapotranspiration, average soil moisture
content, and annual discharge) are a function of total annual
precipitation. Therefore, covariance analysis was conducted on
the hydrologic variables estimated with mean input parameters
and mean plus confidence interval parameters using the covariate precipitation.
Table 2. Soil physical parameters of soil samples collected in ‘La Rosilla’ watershed of Durango, Mexico
(Source: Silva-Flores, 2007).
Where: ASNM = Altitude above sea level (m); P = slope (%), PMO = depth of litter layer (mm); PS = depth of soil (cm); DA = soil
bulk density (g cm-3); DR = soil specific density (g cm-3); CC = field capacity (%); PMP = wilting point (%).
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ESTUDIOYMANEJODELOSRECURSOSNATURALES
RESULTS AND DISCUSION
27.46%).
Soil samples. The average altitude above the sea level
(2736 m) checks well with the distribution range of mixed pineoak temperate forests (Rzedowski, 1978), which is the dominant vegetation type at ‘La Rosilla’. Soil slope is on the average
19%, which can be considered as moderate for this ecosystem
and it is important in the promotion of surface and subsurface
flow. The depth of litter layer is on the average 34 mm, and this
depth is important to control the infiltration rate and the reduction
of surface runoff (Alanis-Morales et al., 2000) in temperate forests. The litter depth also redistributes soil water since this layer
is connected to the mineral soil. Soils have an average depth of
20.9 cm, in agreement with the depth of most Leptosoles that
cover most of the watershed area. Soil bulk density averages
0.82 g cm-3 and it is small in comparison to the bulk density of
most soils dedicated to agriculture and grasslands. High organic
matter contents may explain the small soil bulk density measured. This factor may be also contributing to explain why the field
capacity and wilting point are on the average high (51.3% and
Input parameter values into the model were depth of soil
(20.9 cm), field capacity (0.51) and wilting point (0.27). In addition, the climatic and plant factors considered were 0.75 and
1.25. Interception loss parameters that were employed to run
the model were: c = 0.050; Ec = 2.637 mm h-1; R = 12.66 mm
h-1; P’G = 0.25 mm; Sc = 0.135 mm; and Pt = 0.039.
Annual evapotranspiration and interception loss. For the period of 1945 to 2006, interception loss and actual evapotranspiration had an average, standard deviation, and confidence intervals (α=0.05) of 102 mm, 23.8 mm, and 6.5 mm; and 543 mm,
90 mm, and 24.5 mm, respectively. Large temporal variations,
close to a 100% (Figure 2) were partially explained by the depth
of annual precipitation.
Annual discharge. Average, standard deviation, and confidence interval (α=0.05) of annual discharge were 3.17 M m3,
1.44 M m3, and 0.39 M m3, respectively. Minimum (0.32 M m3)
and maximum (6.67
Figure 2. Interception loss and actual evapotranspiration figures estimated by the mass balance hydrological
model for ‘La Rosilla’ watershed.
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M m3) figures explains also the large temporal variations of
annual discharge. Part of the results of the mass balance hydrological model is reported in Figure 3, which shows the temporal
variations of estimated annual discharge for the period of 1945
to 2006.
There is not information on annual precipitation for the years
1949-1952, 1958, 1980-1982, 1987, 1990, and therefore, these
years miss annual discharge data. Dry spells can be noticed in
the 1950’s and most of the 1990’s (Figure 3). This information is
in agreement with drought episodes reported by Stahle (2001);
Návar (2001; 2004; 2008) for Mexico’s northern forests.
Discharge data distributes normally since maximum deviance between observed and predicted probability was 0.095 and
maximum allowed deviance with an error of 0.05 is 0.20, according to the Kolmogorov-Smirnoff test (Haan, 2003). Using the
mean and standard deviation values for total annual discharge
(3.17 and 1.44 M m3, respectively), in 68 out of 100 years, annual discharge would be between 1.73 and 4.61 M m3. In 15
out of 100 years annual discharge would be less than 1.73 and
larger than 4.61 M m3. Using the confidence interval value, the
long term mean oscillates between 2.78 and 3.56 M m3.
The annual discharge abstraction from ‘La Rosilla’ reservoir
to supply the city of El Salto, Durango amounts to 1.3 M m3 (SIDEAPAS, 2007). This quantity is not enough to meet demands
of this place since the city has a total population close to 22,000
inhabitants and CNA (2005) data reports that the Mexican per
capita water use is 260 liters per inhabitant per day. That is, total
annual demand accounts for 2.07 M m3 and this figure explains
why water is rationalized during several periods of time and for
several places of the city.
Figure 3. Annual discharge estimated by the mass balance hydrological model for ‘La Rosilla’ watershed.
With the use of the normal density function, with the long
term mean and standard deviation of 3.17 and 1.44 M m3 and
the annual demand of 2.07 M m3, there is a 78% chance that
this demand would be met by ‘La Rosilla’ watershed. The rest of
the time, 22%, the administration of the water would be needed
to rationalize water according to the rules set by the municipality
of Pueblo Nuevo or the State of Durango.
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Sensitivity Analysis. Total discharge, mean annual soil moisture content, total actual evapotranspiration, and interception
loss are most sensitive to changes in soil, climatic and plant parameters (Ftv, Fc, cc, and pmp) and they are quite insensitive to
changes in interception loss parameters (Ec, Pt, St, A) (Table 3).
Changes in interception loss from 102.75 mm to 99.26 mm
with changes in all input parameters are of the order of 2%. Total
ESTUDIOYMANEJODELOSRECURSOSNATURALES
actual evapotranspiration is quite sensitive to changes in all input parameters (from 542.78 mm to 440.178 mm) and it attains
a difference ratio of close to 19%. Average soil moisture content
also shifts above 10% when adding the 95% confidence intervals to all input parameters. But total annual discharge is most
sensitive because it shifts close to 38% (from 2.578 M m3 to
3.553 M m3) when adding the 95% confidence interval to mean
input parameters
In fact, the covariance analysis showed that the model slopes that use total precipitation as a covariate were statistically
different, when using average input parameters data in contrast
to when using the mean ± confidence interval slope data was
1.9779 (± 0.228) and when using the mean + confidence interval of input parameters, the slope had a mean value of 1.5685
(± 0.127) (Figure 4).
Table 3. Sensitivity analysis of the mass balance hydrologic model to input parameters for estimating total discharge at ‘La Rosilla’ watershed.
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Figure 4. The covariance analysis that uses total annual precipitation as a covariate to estimate annual discharge
for the watershed ‘La Rosilla’, Durango, Mexico.
Therefore, when using the sensitivity analysis, the annual
discharge would have a range of 2.578 ± 0.975 M m3, between
1.603 and 3.553 M m3. This range is smaller than 2.578 ± 1.25
M m3, when using the average and standard deviation of discharge values. Large variations (from 1 to 8 M m3 are found
with precipitation ranges from 400 to 1400 mm) of the order of
800% are noted in annual discharge with precipitation variations
of 350%. That is, annual discharge varies twice as much as it
does annual precipitation.
Similar findings were observed for total annual interception
loss and actual evapotranspiration, although the covariance
analysis showed similarity between slopes and intercepts (Figure 5). Total average annual evapotranspiration increase twofold
when precipitation increases by threefold (Figure 5).
Soil moisture content is statistically different according
to the covariance analysis since the intercepts deviated unlike
the slopes (Figure 6). Soil moisture content is smaller when the
model is run with mean input parameters and attains a larger
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value when the model is run with average plus confidence interval data. Annual Et is less variable (350 to 700 mm) than annual
discharge.
The watershed ‘La Rosilla’ discharges on the average an
annual volume of 2.578 M m3, while the reservoir ‘La Rosilla
II’ has an ordinary total capacity of 1.5 M m3 and annual demands account for 2.07 M m3. That is, mean annual discharge
and demand are larger than the ordinary storage capacity of
the reservoir. That is, in 81% of the time the watershed would
produce more discharge the reservoir can store. On the other
hand, the model predicts that most runoff is produced during the
presence of important rainfall events, during the wet season and
quite infrequently during the dry season. Although there is not
information on the recession curve of hydrographs they must
be quite flashy and the reservoir has to discharge most rainfall
excess that cannot be stored. Information on the daily storage
variations is required in order to calibrate and better understand
the physical model fitted to this watershed.
ESTUDIOYMANEJODELOSRECURSOSNATURALES
Figure 5. The covariance analysis that uses annual precipitation as a covariate to estimate annual evapotranspiration for the watershed ‘La Rosilla’, Durango, Mexico.
Figure 6. The covariance analysis that uses total annual precipitation as a covariate to estimate average soil
moisture content for the watershed ‘La Rosilla’, Durango, Mexico.
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In the meantime, these observations show that the volume
the reservoir can store must be increased to at least 3.0 M m3
by raising the curtain or building another dam below ‘La Rosilla
II’. Part of the excess water of this reservoir can also be stored
in elevated water tanks placed at the highest points inside the
city of El Salto. A storage management plan must be built up for
‘La Rosilla’ that takes into account the seasonality of discharge,
evpotranspiration, and water supply. This can help to better manage water resources of this watershed.
CONCLUSIONS
This research points out that a mass balance hydrological
model predicts an average interception loss, actual evapotranspiration, soil moisture content and total annual discharge of 102
mm, 543 mm, 0.37, and 2.578 M m3, respectively, when annual
precipitation averages 917 mm at the watershed ‘La Rosilla’,
Durango, Mexico. The model is quite insensitive to interception
loss parameters and most sensitive to soil, climatic, and plant
factors. The model predicts the range of annual discharge values could be between 2.578 ± 0.975 M m3, or between 1.603
and 3.553 M m3. This volume is sufficient to fulfill the storage capacity of the reservoir ‘La Rosilla II’ every year. Although running
the model with a better temporal resolution is required, preliminary conclusions point at increasing the storage capacity of ‘La
Rosilla’ reservoir or opening new sources of storage for excess
blue water.
ACKNOWLEDGMENTS
The author of this report thanks M.C. Ramon Silva Flores
for providing information on the soil sample parameters for the
watershed ‘La Rosilla’.
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Doorenbos, J., and Kassam, A.H. 1979. Yield responses to
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