Determinación
del coeficiente de estratificación horizontal y vertical de la ecuación
modificada de Berlyand
Thuesman
Estuardo Montaño Peralta. Orlando
Hilarión Ãlvarez Hernández.Carlos
Andrés Mora Montaño.Thuesman Humberto Montaño Ramón.
Abstract . <=
span
style=3D'mso-tab-count:2'>Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â=
 DOI: https://doi.org/10.33262/concienciadigital.v4i1.2.1582
This research contributes to
understanding the specific characteristics of the atmosphere in a locality =
to
preserve and conserve people's health, ambient air quality, the well-being =
of
ecosystems and the environment in general. Thus, the purpose of this resear=
ch
is to present the procedure and analysis carried out to obtain the horizont=
al
and vertical stratification coefficient, and to determine the maximum
concentration of pollutants from fixed point sources in the city of Loja -
Ecuador, based on Berlyand's  Through the research methodology, the
predominant stability classes in the city of Loja were determined. Likewise,
the average values of the dispersion parameters were determined. Finally, the value of the coefficient =
A of
the Berlyand
Keywords:
Berlyand model, atmospheric stability, atmospheric
stratification, solar radiation, wind speed.
Resumen.
Esta investigación contribuye al conocimiento de las
caracterÃsticas especÃficas de la atmósfera de una localidad con la fina=
lidad
de preservar y conservar la salud de las personas, la calidad del aire
ambiente, el bienestar de los ecosistemas y del ambiente en general. AsÃ, =
el propósito
de esta investigación es presentar el procedimiento y análisis realizados=
para
obtener el coeficiente de estratificación horizontal y vertical, y determi=
nar
la concentración máxima de contaminantes a partir de fuentes puntuales fi=
jas en
la Ciudad de Loja – Ecuador, a partir del modelo de =
Berlyand .
 Mediante la metodologÃa investig=
ación se
logró determinar las clases de estabilidad predominantes en la Ciudad de L=
oja.
Asà mismo, se determinó los valores promedio de los parámetros de
dispersión. Finalmente, se obtuvo
analÃticamente el valor del coeficiente A para la Ciudad de Loja a
partir de la ecuación de Berlyand
Palabras claves:
Modelo de Berlyand
Introducción.
La contaminación =
del
aire es uno de los grandes problemas que afecta a la mayorÃa de los paÃses
alrededor del mundo, especialmente a aquellos paÃses industrializados y en=
vÃas
de desarrollo. El incremento en las cantidades de gases contaminantes y de
partÃculas potencialmente dañinas para la salud humana y el medio ambient=
e ha
sido constatado a nivel mundial, y la respuesta a estos problemas se centra=
en
la búsqueda de soluciones inteligentes (Delgado, M., et al, 2014), a corto,
mediano y largo plazo, que detengan una contaminación del aire que podrÃa=
ser
irreversible en las próximas décadas.
Los logros obtenid=
os
en la gestión de la calidad del aire contribuyen a la mejora del bienestar
económico y social en muchos paÃses en desarrollo (OMS, 2011). En este se=
ntido,
se ha comprobado que la gestión adecuada de la calidad del aire permite me=
jorar
la salud pública, debido a que la contaminación atmosférica está relaci=
onada
con el aumento de pacientes ambulatorios, principalmente a causa de
enfermedades respiratorias y cardiovasculares, y; por otro lado, al increme=
nto
de admisiones hospitalarias y de la mortalidad diaria.
La Ciudad de Loja =
se
encuentra ubicada al Sur de la República del Ecuador, en el valle denomina=
do de
Cuxibamba , limitando con la cordillera occident=
al de
los Andes. Loja tiene una superficie aproximada de 52 km2 , con
altitudes sobre el nivel del mar entre los 1950 y 2370 m (Fig. 1), y se
encuentra entre las coordenadas siguientes: 03º 39’ 55" y 04º 30â€=
™ 38"
de latitud Sur (UTM 17 S: 9501249 N — 9594638 N); y, 79º 05' 58'' y 79º=
32'
42.1'' de longitud Oeste (UTM 17 S: 661421 E — 711075 E).
Este territorio se
caracteriza por gozar de un clima templado andino, a excepción de junio y
julio, meses en los que se presenta una llovizna de tipo oriental (vientos
alisos) con temperatura que fluctúa entre los 16°C y 25°C. La época de =
mayor
estiaje se presenta entre octubre y diciembre con una precipitación media =
anual
que oscila entre 400 y 1100 mm (GEO, Loja. 2006).
La Ciudad de Loja
tiene una población de 214 855 habitantes y una tasa de crecimiento de 23%,
según lo establece el último censo realizado por el INEC (2010), lo que ha
incidido en una clara expansión de viviendas y con ello la demanda de serv=
icios
que afectan el medio ambiente. Uno de los principales contaminantes que tie=
ne
la ciudad —debido a la urbanización— radica en la explotación de fuen=
tes fijas
estacionarias, tales como los calefones, cuyo combustible o portador energÃ=
©tico
es el gas licuado de petróleo (GLP), el cual emana gases como CO2, CO, NOx , los cuales inciden negativamente en el medio amb=
iente
por constituirse en gases de efecto invernadero (GEI). De igual manera, exi=
sten
ocho fuentes fijas que expulsan a la atmósfera gases de efecto invernadero=
, especialmente
CO2, NOx , y en menor medida SO2 , cuy=
as
ubicaciones se presentan también en la Fig. 1.
Figura =
1. Mapa de la Ciudad de Loja y ubicación de las fuentes puntuales fijas=
.
En la Ciudad de Lo=
ja,
además de la contaminación atmosférica generada por fuentes fijas, exist=
e un
crecimiento sostenido del parque automotor (CEPAL 2008). Por lo general, las
emisiones de una sola unidad de cualquier vehÃculo son muy bajas comparada=
s con
las emisiones de una chimenea industrial, sin embargo, debido a la gran
cantidad de vehÃculos automotores en circulación, representan la fuente
principal de contaminación que, según datos oficiales, en 2017, Loja cont=
aba
con aproximadamente 36 000 vehÃculos en circulación (Agencia Nacional de
Tránsito, 2014).
Aunque la evaluaci=
ón
completa de ubicación de fuentes grandes y especÃficas de contaminación
requiere a menudo información detallada obtenida en el sitio, la informaci=
ón
climatológica para las localidades cercanas puede ser útil en la planific=
ación
preliminar (Holzworth , 1974). Por lo tanto, los=
datos
climáticos son indispensables en la evaluación de medidas de calidad del =
aire
relacionada a las prácticas de control de emisiones y tendencias de calida=
d del
aire. Durante los dÃas de la sem=
ana (es
decir los dÃas de trabajo regulares), cuando las proporciones generales de
emisiones de contaminantes en una ciudad pueden variar poco de dÃa a dÃa,=
las
variaciones observadas en las concentraciones del contaminante son causadas=
por
las variaciones en los rasgos de tiempo pertinentes (H=
olzworth ,
1974). Por otro lado, el ciclo diario del calentamiento y enfriamiento del
suelo bajo la acción de la radiación del sol, asà como la mezcla de masa=
s de
aire de procedencia diferente, tiene como consecuencia la modificación del
valor de la temperatura del aire en función de la altura. Esta modificaciÃ=
³n
repercute en la habilidad de la atmósfera en iniciar o inhibir los movimie=
ntos verticales
del aire (Neiburger , 1969). De esta manera, los=
datos
disponibles requieren un procesamiento especial e interpretación en lo que=
se
refiere a su impacto en el transporte atmosférico y difusión.
Los datos
climatológicos en ocasiones resultan difÃciles de interpretar debido a dos
razones principales. En primer lugar, las observaciones no son en absoluto
hechas en todos los lugares para los cuales se requiere la información, ni=
en
las suficientes locaciones para permitir una interpolación fácil. Por ejemplo, cuando la preocupación e=
s acerca
de la contaminación atmosférica en una ciudad y las observaciones han est=
ado
hechas en un aeropuerto cercano, estos datos deben interpretarse en términ=
os de
los efectos que la ciudad tendrÃa sobre las observaciones (Neiburger ,
1969). Pero, incluso en el caso d=
onde un
sitio de observación está dentro de una ciudad, esas observaciones no pue=
den
ser representativas de todas las secciones de la ciudad. Para una fuente
puntual especÃfica de contaminación es deseable tener las observaciones e=
n la
vecindad inmediata de la fuente. La segunda razón, se debe a que las
observaciones, sobre todo del aire superior, no son hechas con la frecuencia
suficiente. El transporte y caracterÃsticas de la difusión de la atmósfe=
ra cerca
de la tierra (en algunos lugares hasta varios kilómetros) normalmente exhi=
ben
una variación diurna muy grande, que es difÃcil de interpretar en ausenci=
a de
observaciones.
Si bien existen
modelos de dispersión de gases contaminantes recomendados por la USEPA (U.S.
Environmental Protection
Agency), no es menos cierto que los mismos trabajan en función de los =
datos
meteorológicos existentes de cada localidad y los datos meteorológicos a
utilizarse, deberán ser representativos para la ubicación geográfica de =
la
fuente fija a evaluarse. En la Ciudad de Loja no existen estudios de aire
superior, solamente en tres zonas orográficas cuyas condiciones son difere=
ntes
a Loja se ha realizado estudios aerológicos (Montaño, T., 2015).
MetodologÃa .
Se utilizó el sof=
tware
Excel de Microsoft Office para realizar los procesamientos de=
las
diferentes variables meteorológicas, asà como herramientas CAD (Computer Aided =
Design ), especÃficamente el =
software Surfer  Los datos de altitud se interpolaron a=
partir
de los datos del Shuttle Radar Topographic Model (SR=
TM) de
la NASA (National Aeronautics
and Space Administration ).
Las variables
meteorológicas utilizadas normalmente en los estudios de contaminación
atmosférica comprenden la dirección y la velocidad del viento, la tempera=
tura
ambiente, la cantidad de cielo cubierto por nubes, la altura de la base de =
las
nubes, humedad y presión, los cuales son considerados datos meteorológicos
primarios. Por otra parte, los datos secundarios y la forma en la cual son =
identificados
se muestran en la Tabla 1.
Tabla 1. Parámetros meteorológicos secundarios para estudios de contaminaciÃ=
³n
atmosférica
Parámetros
Identificación<=
/o:p>
CategorÃas
de estabilidad atmosférica
Altura
de la capa de mezcla urbana y rural
Exponente
de perfil de viento
Gradiente
vertical y gradiente potencial vertical
Longitud
de Monin-Obukhov
Velocidad
de fricción
Fuente: Turtós y otros, 2004. =
<=
/span>
En el presente
trabajo, se utilizó el modelo de difusión turbulenta de la TeorÃa de Tra=
nsporte
Gradiente
) propuesta por Berlyand (1975)
donde:
, Coeficiente, calculado para condiciones normales de intercambio
vertical y horizontal
, Cantidad de materia expulsad (g.s-1 ). <=
/p>
, Coeficiente adimensional para las condiciones de salida de la mezcla
gas-aire en el punto de emisión. Para expulsiones gaseosas y aerosoles, =
.
, Altura de la fuente (m).
, Volumen de la mezcla gas-aire (m3s-1 ). =
<=
![if !msEquation]>
, Diferencia de temperaturas entre e aire y la mezcla gaseosa.
, coeficientes adimensionales.
La distancia a la cual ocurre la concentración
máxima (
) se calcula considerando la altura de la fuente ( <=
![if !msEquation]>
), el coeficiente adimensional de filtrado ( <=
![if !msEquation]>
), y un parámetro ( <=
![if !msEquation]>
) que depende de la llamada velocidad peligrosa del viento ( =
U m
), la cual es función del volumen de la mezcla gas-aire y de =
.
Debido a que en el presente estudio se pretende
calcular el coeficiente <=
![if !msEquation]>
 para las condiciones de la =
Ciudad
de Loja, y al no contar con los datos primarios ni secundarios, se utilizó=
la
ecuación de concentración máxima propuesta por el Dr. Berlyand ,
la cual requiere un valor de
 adecuado a las condiciones
geográficas y de turbulencia de la zona donde se vaya a aplicar. Para ello=
se
utilizó la ecuación modificada de Berlyand (1994), siendo una más sencil=
la
basada en las caracterÃsticas del intercambio vertical (
) y horizontal (
), que es la usada en el presente trabajo y que expresa:
 =
viene
dado por los valores del coeficiente de intercambio vertical
 =
 y velocidad del viento
 =
a la
altura
 =
=3D 10 m;
 =
es la
dispersión de las fluctuaciones de la dirección del viento para un interv=
alo de
tiempo entre 20 – 30 minutos, para el cual las concentraciones son estima=
das.
Finalmente, para calcular los valores de
,
 =
se
puede utilizar las ecuaciones formuladas por Briggs, según Ulriksen
(2005), que se los detalla en la Tabla 6:
Tabla 6. =
Fórmulas
recomendadas por Briggs según Ulriksen (2005) =
para
 (
) y <=
!--[if gte msEquation 12]>Z
 (
)
CategorÃas de P=
asquill
 (m)
 (m)
CONDICIONES RURALES
A
0.22
 (1+0.0001
 )-0.5
0.20
B
0.16
 (1+0.0001
 )-0.5
0.12h
C
0.011
 (1+0.0001
 )-0.5
0.08
 (1+0.0002
)-0.5
D
0.08
 (1+0.0001
 )-0.5
0.06
 (1+0.0015
)-0.5
E
0.06
 (1+0.0001
 )-0.5
0.03
 (1+0.0003
)-1 <=
/p>
F
0.04
 (1+0.0001
 )-0.5
0.016
 (1+0.0003
)-1 <=
/p>
CONDICIONES URBANAS
A-B
0.32
 (1+0.0004
 )-0.5
0.24
 (1+0.001
)-0.5
C
0.22
 (1+0.0004
 )-0.5
0.20
D
0.16
 (1+0.0004
 )-0.5
0.14
 (1+0.0003
)-0.5
E-F
0.11
 (1+0.0004
 )-0.5
0.08
 (1+0.00015
)-0.5
<=
/span>
El valor de
 =
puede
ser determinado de la relación de la desviación estándar del viento con
respecto al valor medio de los valores medidos cada 30 s (longitud d=
e la
cuerda). Basándose en análisis de escala, bajo condiciones neutras, la al=
tura
de la capa lÃmite suele calcularse a partir de la expresión presentada po=
r Holtslag A.A.M. y van Ulden A.P.
(1983):
Donde
 =
es la
velocidad del viento a la altura de 10 m.Â
El lÃmite superior de la capa superficial se define como la altura =
en la
que
, siendo
 =
la
altura de la capa lÃmite. La lon=
gitud de
Monin – Obukhov se=
calculó
utilizando la ecuación
, donde
 =
es la
constante de Von Karman (0.37) y
 =
es el
lÃmite superior de la capa superficial.
Para el exponente =
de
perfil de viento en terrenos no complejos, Turtós
propone una ecuación hasta una altura de 200 m sobre el nivel del terreno,
considerando que el perfil de viento está razonablemente bien representado=
por
la ley de potencia (Turtós y otros, 2004):
donde
 =
es la
velocidad escalar media de viento a la altura de referencia
, tÃpicamente 10 metros.
Para el caso de la
Ciudad de Loja, la cual se encuentra en un valle entre montañas, con zonas=
de
grandes pendientes, se calculó una longitud de rugosidad orográfica para
determinar si la zona en la cual está enclavada la ciudad se puede conside=
rar
relativamente plana. Esto se real=
izó
confeccionando el Modelo Numérico de Altitud, utilizando los datos del Shuttle Radar Topograp=
hic
Model (SRTM) con resolución de 90 m, al cu=
al
posteriormente se le calculó la desviación estándar para modelar la supe=
rficie
de rugosidad orográfica (Fig. 4), donde se puede observar que la ciudad se
encuentra en una zona con valores casi constantes y aproximadamente igual a
0.1.
El exponente
 =
varÃa
usualmente desde 0.1 en una tarde soleada hasta 0.6 durante noches despejad=
as.
Mientras mayor sea el valor de
, mayor será el gradiente vertical de la
velocidad del viento. Como esta ley de potencia es una aproximación del pe=
rfil
medio de velocidad del viento, los perfiles reales se desvÃan de esta rela=
ción.
Los valores de
, especÃficos para cada sitio, pueden
determinarse con los datos de vientos en dos niveles, resolviendo la ecuaci=
ón
(Turtós y otros, 2004):
En nuestro caso se
utilizaron los datos de viento a las alturas de 10 m y 30 m. El gradiente
vertical y el gradiente potencial de temperatura son usados ampliamente en =
la
modelación de la dispersión de los contaminantes en la atmósfera para
clasificar la estabilidad en la capa superficial, utilizando algoritmos de
parametrización de datos de superfice como la =
altura
de la capa de mezcla y en las ecuaciones de elevación del penacho para
condiciones estables (las de menor porcentaje de ocurrencia en nuestro caso=
).
Estos gradientes se obtienen, internacionalmente, de los sondeos diarios (<=
span
class=3DSpellE>Turtós y otros, 2004). En Ecuador estos sondeos sola=
mente
se realizan en tres lugares, especÃficamente en Guayaquil (5 m de elevacion en costa), isla San Cr=
istóba
(6 m de elevación en Galápagos) y en la estación Nuevo Rocafuerte a una =
altura
de 264 msnm.
La longitud de
rugosidad puede ser calculada a partir de las mediciones de los perfiles de
viento. De hecho, en caso de turbulencia puramente mecánica (por ejemplo, =
con
vientos fuertes), la velocidad del viento promedio u muestra un perfil de
viento logarÃtmico para Z > Z0, el cual está dado por (Panofsky
y Dutton , 1984).
Figura 4. Superficie de rugosidad orográfica para la ciudad de Loja.
El procesamiento de
los cálculos de las Eq . 1 – Eq .
5 se los realizó en una hoja Excel, cuyos resultados importantes se muestr=
an en
la Tabla 7.
Tabla 7. =
Resultados
de los cálculos para la dispersión, la estabilidad atmosférica y el coef=
iciente
 de la ecuación de Berlyand.
. Previo a utilizar los resultados de la
estación meteorológica a dos niveles (10 y 30 m) se utilizó la informaci=
ón del
trabajo sobre estabilidad vertical de la atmósfera en la provincia de Loja
(Ãlvarez, Maldonado y Montaño, 2015) procesando y calculando los valores =
para
la Ciudad de Loja, obteniendo una estabilidad neutra.
Como resultado del
procesamiento de las observaciones de temperatura del aire, y de dirección=
y
fuerza del viento a los niveles de 10 y 30 m obtenidos de la estación
meteorológica automática que se ubicó en los terrenos de la Universidad
Nacional de Loja, durante los meses de enero a marzo de 2015, se obtuvieron,
como promedios, los resultados que se muestran en la Tabla 7, en la cual se
pueden observar los parámetros de dispersión
 =
(
) y
 =
(
), la clase de estabilidad , asà como el =
valor
del coeficiente
 o parámetro
) de la ecuación de Berlyand para el cá=
lculo de
la concentración máxima de gases a partir de fuentes fijas puntual=
es, el
cual resultó con un valor de 83. El valor promedio calculado del parámetr=
o
 se corresponde con lo plant=
eado
por Berlyand (1975) como perteneciente a zonas sin gran turbulencia en las
zonas centrales de la antigua URSS (valor 80), lo cual se cumple en la ciud=
ad
de Loja, en la cual, al contar con de nubes de tipo convectivo, no pasan de
cúmulos promedios en la mayorÃa de los casos, no reportándose tormentas
eléctricas con frecuencia. Adicionalmente, en el perÃodo de mediciones el
promedio de la clase de estabilidad corresponde a la categorÃa neutra.
· =
Adicionalmente a las conclusiones de este trabajo de investigación, =
los
autores recomiendan realizar la modelación a partir de los datos técnicos
medidos en las distintas fuentes, y considerar las matrices de viento (por
valores de velocidad – dirección) como datos de control para el cálculo=
de la
concentración máxima utilizando el parámetro
 calculado para la ciudad de=
Loja.
<=
/span>
Agradecimiento. =
Los autores agrade=
cen
el financiamiento de la Universidad Nacional de Loja a través del proyecto=
de
investigación 28-DI-FEIRNNR-2019
‘Caracterización de la potencialidad de la energÃa solar y eólica e=
n la
Región Sur del Ecuador .’
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El artÃculo que se
publica es de exclusiva responsabilidad de los autores y no necesariamente
reflejan el pensamiento de la Revi=
sta
Ciencia Digital.
El
artÃculo queda en propiedad de la revista y, por tanto, su publicación pa=
rcial
y/o total en otro medio tiene que ser autorizado por el director de la Revista Ciencia Digital.
Facultad de la EnergÃa, Universidad Nacional de Loja, Loja, Ecuador, juan.=
solano@unl.edu.ec
Facultad
de la EnergÃa, Universidad Nacional de Loja, Loja, Ecuador, milton.leon@un=
l.edu.ec
Facultad de Ciencias
Agropecuarias, Universidad Técnica de Machala, Machala, Ecuador, wtorres@u=
tmacha.edu.ec
IngenierÃa
Mecánica, Universidad Politécnica Salesiana, Cuenca, Ecuador, thuesman92@=
gmail.com
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