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Artículo científico / Research paper
Modelado
hidrológico de un páramo andino venezolano con afloramientos rocosos usando
TOPMODEL
Hydrologic modeling of a Venezuelan Andean páramo =
with
rocky outcrops using TOPMODEL
Marilena Y=
eguez1,2
, Magdiel =
Ablan1
, Wouter
Buytaert3
, Dimas Ac=
evedo4 ,
Mayanín E. Rodríguez4 , Daniel Machado4
Centro de Simulación y Modelos (CESIMO),
Universidad de los Andes, Mérida, Venezuela.
Laboratorio de Prototipos, Universidad
Nacional Experimental del Táchira, San Cristóbal, Venezuela.
Ingeniería Civil y Ambiental, Imperial Co=
llege
London, Londres, Reino Unido.
4 Instituto de Ciencias Ambientales y Ecol=
ógicas
(ICAE), Universidad de los Andes, Mérida, Venezuela.
Autor para correspondencia: mariyeg@gmail.com
Fecha de recepción: 15 de jul=
io
de 2019 - Fecha de aceptación: 30 de septiembre de 2019
RESUMEN
Los afloramientos rocosos en el páramo a=
ndino
venezolano constituyen una unidad geomorfológica con un área considerable. =
Los
procesos hidrológicos de esta área fuente no son representados por TOPMODEL.
Por lo tanto, este estudio tuvo por objetivo mejorar la simulación hidrológ=
ica
de TOPMODEL, específicamente la descripción del flujo superficial, mediante=
la
incorporación de flujo de este tipo generado por el área fuente rocosa. Bas=
ado
en el análisis de varias investigaciones, un parámetro a fue introducido para redireccionar a f=
lujo
superficial una fracción de la precipitación que cae sobre los afloramientos
rocosos. Este parámetro fue calibrado, lo que condujo a una
mejora de la eficiencia Nash-Sutcliffe en las fases de calibración y valida=
ción
del modelo. Asumiendo un coeficiente de escorrentía de 1 en los afloramient=
os y
de acuerdo con la calibración, la
lluvia que cae en un 25% del área de afloramientos es redireccionada,
posiblemente se trate del conjunto de afloramientos ubicados a lo sumo a 44=
m
de la red de drenaje. Sin embargo, otras interpretaciones son posibles, lo =
que
requiere más investigación.
Palabras clav=
e : TOPMODEL, modelado de cuenca, páramo andino, afloramientos
rocosos.
ABSTRACT
The rocky outcrops in the Venezuelan Andean páramo constitute a
geomorphological unit with a considerable area. The hydrologic processe=
s of
this source area are not represented by the TOPMODEL. This study aimed to
improve the hydrological simulation of
the TOPMODEL, specifically the description of overland flow, by
incorporating flow of this type generated by the rocky source area. Based on
the analysis of various researches a parameter a was introduced redirecting=
to
overland flow a fraction of the precipitation falling on the rocky outcrops.
This parameter was calibrated, what led to an improvement in Nash-Sutcliffe
efficiency in the model calibration and validation phase. Assuming a runoff
coefficient of 1 in the outcrops and according to the calibration, the rain=
fall
that falls on 25% of the outcrop areas is redirected, possibly it is the se=
t of
outcrops located at most 44 m from the drainage network. However, other
interpretations are possible, what requires further research.
Key=
words : <=
/span>TOP=
MODEL,
catchment modeling, Andean páramo, rocky outcrops.
1. INTRODUCCIÓN<=
/o:p>
Los estudios
hidrológicos del páramo han sido desarrollados principalmente en Ecuador y
Colombia. Estos páramos presentan marcadas diferencias en sus componentes
biofísicos respecto a los páramos venezolanos que se caracterizan por ser
páramos climáticamente estacionales y secos; con relieves abruptos y
porcentajes importantes de afloramientos rocosos; con suelos jóvenes,
graníticos, arenosos, poco profundos, sin estructura y de baja retención de
agua; con un sistema en rosario de humedales y lagunas con alta conectividad
hídrica. Por tal razón, existe un vacío en el conocimiento hidrológico de l=
os
páramos venezolanos que no puede suplirse de forma directa con los estudios
desarrollados en Colombia y Ecuador (Rodrí=
guez,
2010) . Una de las características distintivas de los páramos venezol=
anos
es la presencia de afloramientos rocosos, conocidos como parte del lecho rocoso o de otro estrato que
sobresale por encima de los sedimentos o del suelo que lo recubren (OMM & UNESCO, 2012) .
Una descripción =
de la
respuesta de los afloramientos rocosos a la lluvia y los diferentes factores
que la controlan es presentada por Woo (20=
12) ,
si la superficie
de la roca es
impermeable y sin almacenamiento en la superficie, y la evaporación es
insignificante, se puede producir un coeficiente de escorrentía de 1.0. Esta
relación rara vez se alcanza por varias razones. El aumento del ancho de las
fracturas aumenta la infiltración y reduce la escorrentía superficial. La
disponibilidad de almacenamiento en la superficie de la roca retiene un poc=
o de
agua de lluvia. Incluso después de que se libere el exceso de agua, se
satisfacen los requisitos de almacenamiento del afloramiento cuesta abajo a=
ntes
de que pueda continuar la escorrentía. La disminución de la intensidad de la
lluvia y el aumento de la duración del evento ofrecen más tiempo para la
infiltración y para la evaporación. Las altas tasas de evaporación son
efectivas para eliminar la película de agua producida por la lluvia en la
superficie de la roca y para agotar el agua contenida en las depresiones de=
la
superficie. Estos factores no son necesariamente independientes entre sí.
A una escala de =
cuenca,
la escorrentía de los afloramientos forma parte de la escorrentía directa o
componente de escorrentía rápida (junto con la precipitación directa en el
canal y el flujo superficial desde zonas selladas y saturadas) contribuyend=
o en
más de un 41% a la escorrentía total, durante condiciones de cuenca húmeda =
(Suarez, Okello, Wenninger, & Uhlenbrook, 20=
15) .
Un estudio más revelador es el de Burns et al. (2001) donde la
escorrentía de un afloramiento que ocupa cerca de un tercio de las 10 ha de=
una
cuenca en Georgia, dominó la escorrentía de caudal en condiciones de flujo
máximo durante dos eventos de precipitación en el invierno de 1996. Este
resultado difiere de los reportados en la mayoría de otros estudios, en cue=
ncas
forestales pequeñas, en las cuales el agua antigua o el agua subterránea
dominan el flujo pico.
Se han modelado =
con
TOPMODEL pequeñas cuencas caracterizadas por la presencia de afloramientos
rocosos, obteniéndose ajustes buenos y aceptables respectivamente (Durand, Robson, & Neal, 1992; Seibert, Bish=
op,
& Nyberg, 1997) . Pero el comportamiento hidrológico de los
afloramientos no fue modelado, para empezar el modelo usado es incapaz de
distinguir dichas unidades geomorfológicas. Tampoco se reportó información
sobre la extensión, ubicación u otras características de los mismos.
Un modelo que sí
representa el comportamiento hidrológico de los afloramientos rocosos es el
descrito y probado por Tarolli, Borga, &am=
p;
Fontana (2008) se trata de un modelo de deslizamiento superficial, q=
ue
utiliza un índice de humedad cuasi dinámico para predecir la distribución
espacial de la saturación del suelo en respuesta a una lluvia de duración
específica. Como las partes superiores del paisaje están caracterizadas por
afloramientos rocosos, se toma en cuenta las diferentes velocidades de
propagación de la escorrentía a través de la roca desnuda y los elementos
topográficos del suelo. El modelo se aplica en una cuenca en los Alpes
italianos (1.47 km2 ), con afloramientos de roca de un 28%. Se
determina que el modelo ofrece una mejora considerable con respecto al mode=
lo
cuasi dinámico no generalizado y el modelo de estado estacionario para pred=
ecir
deslizamientos de tierra.
Lanni,
McDonnell, & Rigon (2011) fomentan el uso de su índ=
ice
topográfico dinámico suavizado para describir el componente de flujo
subsuperficial lateral en modelos de generación de deslizamientos de tierra=
y
modelos conceptuales de lluvia-escorrentía; en contraposición a los índices
topográficos derivados de la suposición de estado estacionario (especialmen=
te
cuando hay disponibles modelos de elevación digital de alta resolución).
Según Wilson & Gallant (2000) la idoneidad de estos índices como
herramientas de aplicación general aún tiene que ser demostrada. Por lo tan=
to,
e xiste la necesid=
ad de seguir buscan=
do
representaciones apropiadas, modelos que simulen la escorrentía y cuantifiq=
uen
el efecto de los afloramientos rocosos. Los modelos en general son una
herramienta útil para probar hipótesis sobre un sistema, inclusive en siste=
mas
hidrológico (Buytaert & Beven, 2011) . En la actualidad, una variedad de
modelos hidrológicos, están
siendo usados por la comunidad científica. Uno de estos modelos, TOPMODEL,
concebido para pronóstico hidrológico en zonas templadas húmedas, intenta
combinar los importantes efectos distribuidos de la topología de la red de
canales y áreas de contribución dinámica con las ventajas de los modelos de
cuenca simples con parámetros agregados (B=
even
& Kirkby, 1979) .
TOPMODEL se ha usado para un primer intento de modeli=
zación en el valle principal de una microcuenca de páramo venezolano (Yeguez, Ablan, Acevedo, Rodríguez, & Machad=
o, 2018) ; por ser un modelo hidrológico de base física (Durand et al. , 1992) , adecuado pa=
ra modelar el proceso de lluvia-escorrentía en cuencas con suelo poco profu=
ndo y topografía moderada (Devi, Ganasri, & Dwarakish, 2015) , =
que fue usado satisfactoriamente en el páramo ecuator=
iano y colombiano (Buytaert & Beven, 2011; Gil & Tobón, 2016) . Si bien dicho val=
le se caracteriza por una marcada estacionalidad, los resultados obtenidos =
de la implementación de TOPMODEL no son del todo inaceptables, por lo que u=
na mejor representación de los picos del hidrograma y un desplazamiento ver=
tical de la curva de recesión pudieran hacer coincidir el hidrograma simula=
do con el observado. Una manera de mejorar dichos resultados podría ser la representación de=
características de la cuenca que el modelo no considera, como es el caso d=
e los afloramientos rocosos, que parecen influir de manera importante en la=
respuesta de la cuenca. Por lo tanto, TOPMODEL debe adaptarse para una ade=
cuada simulación del proceso de lluvia-escorrentía en páramos con afloramie=
ntos rocosos. Afortunadamente, un número suficiente de desarrollos y cambio=
s en los principios básicos del TOPMODEL original que han sido hechos, perm=
iten describirlo como un "enfoque" en lugar de un modelo específi=
co (Seibert et al. , 1997) . la verificación de campo=
ha
mostrado que en el páramo el índice topográfico de TOPMODEL puede identific=
ar
las áreas saturadas. Este es el resultado de los gradientes de pendiente cl=
aros
y los suelos poco profundos de las cuencas (Buytaert
& Beven, 2009) . Ya q=
ue
estas características se presentan en el área de estudio, y dada la
versatilidad del modelo TOPMODEL, esta investigación se propone modificarlo
para incluir la representación de afloramientos rocosos, constituyéndose en=
un
intento por modelar explícitamente
la hidrología de estas unidades geomorfológicas en cuencas de páramo andino,
unidades que también están presentes en el páramo ecuatoriano (Buytaert,
Iñiguez, & De Bièvre, 2007; Buytaert & Beven, 2009; Buytaert & Beven, 2011) .
2. =
MATERIALES
Y MÉTODOS
En e=
ste
apartado se presenta una breve descripción del área de estudio, de la
estructura básica y principales flujos de TOPMODEL y de la modificación lle=
vada
a cabo. También se abordan otros aspectos, como los datos que estuvieron
disponibles para el modelado y el preprocesamiento que estos requirieron.
Finalmente, se describen las etapas del proceso de modelado que fueron
cubiertas como parte de esta investigación.
2.1. Área de
estudio
El área =
de
estudio es el valle principal de la microcuenca de la quebrada de Miguaguó,
sector Mixteque en
Mérida, Venezuela, superficie de 3.62 km2 sobre los 3600 m de
altitud. Las precipitaciones allí presentan un régimen unimodal, con una
marcada estacionalidad de dos a tres meses secos. El promedio anual de
precipitación es 1170 ± 125 mm . Los eventos de precipitaci=
ón son
en promedio de 7 mm solamente (Rodríguez,
Acevedo, Buytaert, Ablan, & De Bièvre, 2014) , se caracterizan por
ser de baja magnitud, poca intensidad y alta frecuencia (Rodríguez, 2010) . Por otra parte, la radiación solar=
es
fuerte 1200 W m-2 , especialmente durante la estación seca (Córdova, 2014) .
Las formas de relieve domina=
ntes
son los till sobre laderas, unidad que abarca el 53% del área, seguido luego
por los afloramientos rocosos (18%), till sobre el fondo de valle (17%) y
lagunas y humedales sobre cubetas de sobre excavamiento (8%). El resto del =
área
lo representan morrenas de retroceso y derrubios rocosos (Rodríguez et al ., 2014) . Pero, se=
gún Córdova (2014) la unidad geomorfológica
dominante es la ladera con manto coluvial (45%), seguido por afloramiento
rocoso (20.2%). Según ambos autores y a pesar de las diferencias en los
porcentajes, los afloramientos rocosos ocupan un segundo lugar. En la Figur=
a 1
se muestran las distintas unidades geomorfológicas presentes en el área de
estudio y seis clases de gradiente de la pendiente. Siendo la clase 30-60%,
escarpado según la FAO (2009) , la de mayor ocupación espacial=
(37%
de la superficie total).
En los suelos hay predominan=
cia de
una alta fracción esquelética o gruesa sobre la fracción fina. En la fracci=
ón
fina es la arena la que predomina, lo cual resulta en texturas gruesas (Fra=
nco
arenoso y areno francoso). Además, los suelos en su horizonte superficial
presentan alto contenido de materia orgánica de un 8 hasta 28%, estrechamen=
te
ligado a las pendientes; las pendientes menores a 5% tienen los mayores val=
ores
de materia orgánica (suelos de orden Histosol y suelos minerales del orden
Inceptisol y algunos con características superficiales hísticas), y a medida
que aumentan las pendientes disminuye los contenidos de materia orgánica
(suelos minerales jóvenes, Entisoles e Inceptisoles) (Córdova, 2014) .
Toda el área de estudio posee
vegetación natural. La
vegetación está conformada por arbustales-rosetales bajos, arbustales altos,
humedales y bosques altoandinos. El tipo de
vegetación dominante es el arbustal-rosetal bajo, el cual se distribuye
uniformemente sobre toda el área. Las otras formaciones vegetales se dispon=
en
en parches, inmersas dentro de la vegetación anterior. La vegetación en la
ladera derecha es predominantemente
Figura 1. =
a) =
U nidades
geomorfológicas ;=
b) =
G radiente de la
pendiente en el área de estudio. Fuente: C=
órdova
(2014) ajustado.
un
arbustal-rosetal con un dosel espeso. Por otra parte, los fondos de valle y=
la
ladera izquierda están cubiertos por un arbustal de dosel abierto con mayor=
es
porciones de suelo desnudo. Mientras que los humedales están dominados por
vegetación de céspedes y ciénagas (Rodrígu=
ez,
2010) , conformando estos un sistema en rosario junto a las lagunas <=
span
style=3D'mso-no-proof:yes'>(Rodríguez et
al. , 2014) .
2.2. TOPMODEL
Se u=
só una
implementación en R de TOPMODEL, basada en la versión FORTRAN de Keith Beve=
n de
1995 (Buytaert, 2009) , cuyo código =
se
encuentra disponible en la plataforma GITHUB ( https://github.com ). Su estructura y=
los
flujos más importantes son ilustrados en la Figura 2a.
En p=
rimer
lugar, se calcula el flujo para infiltración, f , a partir de la precipitación y usando el modelo Green y Ampt
(1911). Dicho flujo ingresa al suelo por medio de un primer compartimiento
denominado zona radicular. Además, se calcula el flujo superficial por exce=
so
de infiltración, fex , como la
diferencia entre la precipitación y f. La
evapotranspiración, Ea , es calc=
ulada como
una función de la evapotranspiración potencial y el almacenamiento de humed=
ad
de la zona radicular. Cuando la capacidad de la zona radicular es superada,
todo el flujo pasa al compartimiento de la zona no saturada. Si el contenid=
o de
humedad de la zona no saturada es mayor al déficit de la zona saturada, se
determina el exceso y este permite calcular el flujo superficial por
saturación, q0 . Además, si hay
déficit de la zona saturada, se genera un flujo vertical hacia el
compartimiento de dicha zona, que depende de la profundidad del nivel freát=
ico
y que a lo sumo llega a ser el contenido de humedad del compartimiento de la
zona no saturada. Finalmente, se calcula el flujo en la zona saturada, qs .
En TOPMODEL se hace uso del =
Índice
Topográfico de Kirkby (a /tan β ) para identificar los puntos en la cuenca capaces de desarrol=
lar
condiciones de saturación y definir las áreas de contribución. Las <=
span
lang=3DES style=3D'mso-bidi-font-size:9.0pt'>suposiciones básicas, subyacen=
tes al
índice, en las que se basa el modelo son: 1) La dinámica de la zona saturad=
a puede
ser aproximada por representaciones de estado estable sucesivas de la zona
saturada en un área a drenando a un punto en la ladera. 2) El gradie=
nte
hidráulico de la zona saturada puede ser aproximado por la pendiente
topográfica de la superficie local, tan β . Una suposición adicional, el p=
erfil de
transmisividad puede ser descrito por una función exponencial del déficit de
almacenamiento, Di , =
con un
valor de T0 cuando el
suelo está saturado en la superficie (Beve=
n,
2012) . Bajo estas suposiciones es descrito qs, el mismo qsi
de las ecuaciones 1 y 2 (donde m es un
parámetro que controla la tasa de disminución de la transmisividad con
incremento del déficit de almacenamiento y r
una tasa de recarga espacialmente homogénea). Además, las suposiciones permiten verific=
ar la
relación entre la profundidad del nivel freático local y el índice topográf=
ico
en ese punto. El cálculo requerido por TOPMODEL para generar un patrón de n=
ivel
freático local espacialmente distribuido se reduce a un cálculo para cada c=
lase
de índice topográfico.
Finalmente,
qs permite determinar el flujo =
base.
Mientras que los flujos fex y q0 constituyen el flujo superficia=
l.
Según la literatura, los conceptos de TO=
PMODEL
no son aplicables en todas partes, debido a que los supuestos básicos
subyacentes al índice se rompen particularmente en cuencas sujetas a una fu=
erte
estación seca (Beven, 2012). A pesar de esto y de la fuerte estacionalidad =
presente
en el área de estudio, dichos sup=
uestos
no se cuestionan en este trabajo. En todo caso se está planteando la necesi=
dad
de una mejor representación del comporta=
miento
dinámico de los caudales, que pudiera lograrse con la representación del
comportamiento hidrológico de los afloramientos rocosos. Según Rodríguez et al. (2014) el
comportamiento dinámico
Figura 2. a) Estructura y flujos de TOPMODEL; b) Estructura y flujos de TOPMOD=
EL
modificado.
(fuertemente dependiente de las precipitaciones en la ép=
oca
húmeda) debe estar asociado a la gran superficie de afloramientos rocosos,
unidad sobre la que escurre la totalidad de las precipitaciones que recibe;=
y
por otra parte a las laderas que son incapaces de retener gran parte del ag=
ua,
al menos en los primeros 10 cm de profundidad. Las laderas podrían estar
sujetas entonces a procesos de infiltración y rápida escorrentía subsuperfi=
cial
(Rodríguez, 2010; Córdova, 2014) . Sin embargo, durante la época seca se podría
presumir un menor efecto de los afloramientos rocosos. Ya que el caudal no =
es
tan sensible a las precipitaciones, pudiendo ser el resultado de bajos
potenciales matriciales en los suelos, que retienen una gran parte de las p=
ocas
precipitaciones que ingresan y generan bajo drenaje (Rodríguez et al. , 2014).
Por otro lado, la conectivid=
ad
hídrica existente entre las laderas, lagunas y humedales contribuye a la
recarga lenta y constante de las unidades de fondo de valle, cuyos <=
span
lang=3DES style=3D'mso-bidi-font-size:9.0pt'>suelos son los que mayor capac=
idad de
almacenamiento de agua ofrecen, gracias a su alto contenido de materia orgá=
nica
(Córdova, 2014) . Adicionalmente, los
suelos orgánicos de los humedales mantienen elevados contenidos de agua
permanentemente (Rodríguez et al. , 2014) . Estas unidades de fondo de valle, las zon=
as
donde se ubican los humedales y las lagunas han de ser consideradas por el
índice topográfico como propensas a saturación y el resto como menos propen=
sas.
La mayoría de los afloramientos rocosos han de ser etiquetados como menos
propensos a saturación por su ubicación, y al considerarlos de esta forma o
inclusive como propensos a saturación se modelaría un comportamiento que no=
se
corresponde con el que estas unidades geomorfológicas realmente exhiben. Po=
r lo
tanto, la modificación de la estructura de TOPMODEL que se propone (Figura =
2b)
consiste en redireccionar a flujo de afloramiento, a , una proporción del flujo que infiltraría.
2=
.3. Datos disponibles y preprocesamiento=
Se dispuso de un modelo digital de elevaciones y una serie de datos de precipitación,
caudal y evapotranspiración, provenientes de un=
sistema
de monitoreo que fue implementado en el área de estudio en el año 2008
(Rodríguez, 2010) .
El modelo digital de elevaciones usado tiene una resolución de 5 m, =
este
requirió la eliminación de sumideros, razón por la que se usó la función sinkfill
del paquete TOPMODEL.
Los datos de cau=
dal se
estimaron a partir de mediciones hechas cada 10 minutos en un vertedero
triangular (90°), ubicado en el punto de salida del valle. Se identifican d=
os
grandes discontinuidades de datos de caudal antes de abril de 2011, razón p=
or
la que se define el periodo 01/09/2011-31/03/2012 para calibración y del
01/09/2012 al 31/03/2013 para validación. Además, porque dichos periodos se
corresponden a los mismos siete meses simulados en Yeguez et al. (20=
18),
que incluyen meses húmedos, secos y de transición. La serie para calibració=
n se
caracteriza por caudal mínimo de 1e-07 m/10 min
Los datos de precipitación corresponden a mediciones hechas cada 10 mi=
nutos
por una estación climatológica automatizada (r esolución mín=
ima
0.2 mm) , instalad=
a en el
fondo de valle del área de estudio. La serie para calibración se caracteriza por precipitaci=
ón
media de 1.51e-05 m/10 min y precipitación máxima de 3.14e-03 m/10 min. En
validación la media fue 8.40e-06 m/10 min y la máxima 3.1e-03 m/10 min.
Los datos de precipitación y caudal fuer=
on
almacenados en archivos de texto para ser leídos en R, como una serie de da=
tos
asociada a una secuencia temporal de 10 minutos. Lo que requirió identificar
los datos faltantes, un 11% en la serie de caudal para validación. Estos fu=
eron
completados mediante interpolación lineal. Respecto a las series de
precipitación no se identificó discontinuidades.
Los datos de evapotranspiración usados s=
on
estimaciones diarias de evapotranspiración de la vegetación ajustada a
condiciones de estrés hídrico, calculada con el método de la FAO. Se prefie=
re
esta estimación sobre la evapotranspiración de referencia, ya que esta últi=
ma
sobreestima en gran medida las salidas por este flujo, principalmente duran=
te
la época de sequía (Rodríguez, 2010).
Cada estimación diaria se distribuyó en 144 valores, uno por cada 10 minuto=
s,
por medio de una distribución normal, imitando la función approx.pe.ts <=
/i>del
paquete DYNATOPMODEL de R (Metcalfe, Beven,
& Freer, 2016) .
2.4. Calibración y validación
Como en general =
no es
posible estimar todos los parámetros de un modelo por mediciones directas o
estimaciones previas, se usó para la calibración la simulación de Monte Car=
lo,
que implica múltiples ejecuciones del modelo usando diferentes conjuntos de=
valores
de los parámetros escogidos al azar (Beven,
2012) . Algunos de estos parámetros se asocian a condiciones iniciale=
s,
tal como sucede en Buytaert & Beven (2011) y Gil & Tobón (2016) =
.
Con la finalidad de poder
establecer comparaciones se realizaron dos calibraciones, una antes y otra
después de la modificación del modelo, usando la función topmodel del
paquete TOPMODEL. Para cada calibración se realizaron 10,000 ejecuciones del
modelo, usando las series de datos correspondientes al periodo 01/09/2011-3=
1/03/2012
y comenzando con los rangos de valores para cada parámetro propuestos por <=
span
style=3D'mso-no-proof:yes'>Buytaert & Beven (2011) , que también =
fueron
usados por Gil & Tobón (2016) . =
Las
descripciones de los nueve parámetros calibrados (qs0 , lnTe , =
m ,
Sr0 , Srmax , td , vr , k0 , CD ) y los
rangos finales de calibración para ambos casos se muestran en la Tabla 1.
Los rangos finales de calibración se
obtuvieron ajustando los rangos sin afectar el desempeño de los modelos. Con
cada ejecución de la función topmod=
el se
obtuvo una matriz de descargas simuladas (con cada columna representando la=
s descargas
asociadas a un conjunto de parámetros) y un arreglo de eficiencias de Nash-Sutcliffe , una eficiencia =
para
cada conjunto de parámetros, lo que
permitió evaluarlos así como también evaluar los modelos. La eficiencia de
modelado de Nash-Sutcliffe es una medida cuantitativa de bondad de ajuste,
también conocida como función objetivo o medida de rendimiento, ampliamente
utilizada, basada en la varianza del error, que alcanza el valor de 1 para =
un
ajuste perfecto (Beven, 2012) .=
Adicionalmente, se usó el método GLUE (p=
or sus
siglas en inglés, Generalized Likelihood Uncertainty Estimation) para gener=
ar
límites de incertidumbre por medio del cálculo de cuantiles ponderados a pa=
rtir
de las predicciones de una batería de conjuntos de parámetros comportamenta=
les.
Ya que algunas veces un modelo puede lograr eficiencias Nash-Sutcliffe
razonables, pero ser incapaz de generar límites de incertidumbre del 90% us=
ando
conjuntos de parámetros razonables (Buytaert & Beven, 2011).
Para la validación de los modelos TOPMOD=
EL y
TOPMODEL modificado se usaron pruebas de regist=
ro
dividido, tal como hicieron Buytaert
& Beven ( 2011) y Gil & Tob=
ón (2016) . Una prueba de registro dividido consiste en hacer qu=
e el
modelo use parámetros estimados en un primer periodo para predecir un
segundo periodo, que en este caso corresponde a uno de la misma longitud del
periodo de calibración, solo que un año después (01/09/2012-31/03/2013).
3. RESULTADOS Y DISCUSIONES
Usando la función topidx de TOPMODEL se calculó el índice
topográfico (ver la Figura 3a). Se puede apreciar que predominan los valores
bajos. Mientras que los altos se localizan en fondo de valle, que son las z=
onas
más propensas a saturación, donde se encuentra la red de drenaje, los humed=
ales
y las lagunas. Ya que las unidades de afloramientos rocosos se encuentran
distribuidas a lo largo del área de estudio, estas son caracterizadas con
valores de índice en todo su rango, tal como muestra el gráfico de barras d=
e la
Figura 3b, generado a partir del cruce de un mapa de afloramientos rocosos =
y el
mapa del índice topográfico.
A pesar de que los afloramientos rocosos deberían permitir un
escurrimiento de toda el agua que cae sobre ellos, a la mayoría se les asig=
na
valores bajos del índice; es decir, se consideran zonas no propensas a la
saturación, generándose flujo subsuperficial que si bien sería menor al que=
se
produciría en un área saturada, pudiera ser la razón por la que se tiene
sobreestimación del flujo base.
Para las calibraciones, la función topmodel requirió además de las series de
precipitación, caudal y evapotranspiración, una matriz con datos de las cla=
ses
del índice topográfico (que se generó con la función make.classes del paquete TOPMODEL ) y =
la
función de retardo (que se generó con la función build_routing_table del
paquete DYNATOPMODEL de R).
La
calibración de TOPMODEL se puede ver en la Tabla 1, donde se presenta el
conjunto de parámetros correspondiente a la mejor eficiencia obtenida y el
rango final de estos. La =
mayoría
de los rangos de los parámetros mantuvieron en los valores iniciales o se
acotaron luego de analizar los resultados de corridas preliminares. En el c=
aso del parámetro=
Srmax se baja el límite inferior y=
para td se define un nuevo rango.<=
/o:p>
=
Figura 3. a) Índice
topográfico en el área de estudio; b) Valores de índice asignados a los
afloramientos rocosos.
Se o=
bservó
que TOPMODEL no estaba simulando la totalidad de los eventos de precipitaci=
ón
debido a altos valores de Srmax , de
este parámetro depende
que el agua en la zona radicular pase o no al drenaje de la zona no saturad=
a. Srmax está asociado a la capacidad de campo =
(Beven & Kirkby, 1979) , citando a Rodríguez (2010) el porcentaje de carbono
orgánico presente en los suelos de Venezuela es menor al de los suelos de
Ecuador y Colombia. Además, se han reportado correlaciones altamente
significativas entre la cantidad de carbono orgánico en el suelo y su capac=
idad
de campo.
La
disminución del límite inferior del parámetro Srmax , plenamente justificada, implicó
la diminución del límite superior de Sr0, ya que este último parámet=
ro
se encuentra supeditado por el p=
rimero .
Estos cambios mejoraron la representación de eventos de precipitación y las
eficiencias en consecuencia, pero trajo consigo una considerable disminució=
n de
los flujos de evapotranspiración simulados, ya que son precisamente estos
parámetros los que participan en la determinación de la evapotranspiración.=
Por ot=
ro lado,
en los primeros intentos de modelado de una cuenca de páramo ecuatoriana se
reportó insensibilidad del parámetro td , razón por la que se eliminó
argumentando que de esa forma se simplifica el modelo, quedando la zona no
saturada y saturada unidas. En los suelos orgánicos del páramo es difícil
distinguir el borde entre la zona saturada y la no saturada debido a las
propiedades de expansión y contracción de los suelos, y la alta capacidad de
almacenamiento de agua en condiciones insaturadas (Buytaert & Beven, 2009) . El parámetro también resultó
insensible en el modelado de una cuenca colombiana (Gil & Tobón, 2016) . Según Güntner,
Uhlenbrook, Seibert, & Leibundgut (1999) td es parte de una formulación muy simple del movimiento vertic=
al
del agua del suelo y no tiene contrapartida física directa. Sin embargo, un
valor alto de td se justifica s=
i se
tiene un valor alto de T0 (gran
permeabilidad de los suelos) para que se produzca algún retraso en el
movimiento del flujo entre la zona no saturada y la saturada (Oberto, 2006) . Esto se observó en dos cu=
encas
mediterráneas, con condición seca, donde los valores calibrados fueron 10.3=
2 y
10.4 respectivamente (Piñol, Beven, & =
Freer,
1997) .
Un val=
or alto
para td, así como un valor bajo=
de vr
propician un retardo del flujo. En
una cuenca ecuatoriana el valor calibrado de vr fue 750 m/h, muy lento comparado con las estimaciones de cam=
po.
Lo que se atribuyó a la falta de un tercer reservorio fuertemente relaciona=
do
con grietas y macroporos (Buytaert, Céller=
i, De
Bièvre, Deckers, & Wyseure, 2004) . En el caso del páramo venezol=
ano,
se presumiría entonces mayor necesidad de un tercer reservorio, ya que los
valores calibrados de vr son mucho más bajos. Otra posible explicaci=
ón
para este comportamiento podría ser la presunción de estado estacionario de=
la
zona saturada, sobre la que se fundamenta TOPMODEL. El retraso sería un
mecanismo usado por el modelo para sincronizar lo observado y simulado.
En dif=
erentes
corridas de calibración los valores de los
mejores conjuntos de parámetros fueron muy similares, salvo el caso de k0 y CD . Dichos parámetros son usados e=
n la
rutina de infiltración, y a partir del flujo que infiltra se determina el f=
lujo
sobre la tierra por exceso de infiltración. Por lo tanto, ambos flujos han =
de
ser variables en las diferentes corridas; siendo muy bajo el flujo sobre la
tierra por exceso de infiltración, en todos los casos.
La representación del comportamiento hidroló=
gico
de los afloramientos rocosos en TOPMODEL requirió redireccionar un porcentaj=
e del
flujo que infiltra a flujo superficial. Por lo tanto, se agregó un parámetro adicional, a , la proporción de flujo de precipitación a redireccionar. Dic=
ho
parámetro se fijó inicialmente en 0.20, por ser aproximadamente el área que
cubren los afloramientos rocosos, pero al observar un bajo desempeño del mo=
delo
se decidió calibrarlo también. Las mejores eficiencias fueron obtenidas usa=
ndo
valores de a entre 0.04 y 0.05
inclusive.
En la Tabla 1 se muestra la calibración del
TOPMODEL modificado usando a =3D=
0.05,
específicamente la eficiencia obtenida y los valores del resto de parámetros
(manteniendo los rangos usados para la calibración de TOPMODEL). Se puede
observar que la modificación hecha al modelo mejora la eficiencia en
calibración. Mejores resultados se obtuvieron ampliando el límite superior =
de qs0 y de Sr0 (condiciones iniciales) , con el respectivo aumento del límite inferior de Srmax. Al conservar los rangos o al ampliarlos, los mejores valores =
de
los parámetros se mantuvieron muy similares en las diferentes corridas, con=
las
excepciones k0 y CD , como suce=
dió
con TOPMODEL.
La Figura 4 muestra el caudal observado =
y el
simulado por TOPMODEL y TOPMODEL modificado luego de la calibración. Se obs=
erva
que TOPMODEL modificado hace en general una mejor representación de los pic=
os y
las curvas de recesión, aun cuando estas últimas siguen sobreestimadas está=
n la
mayor parte del tiempo más próximas a los datos observados que sus pares de
TOPMODEL.
Figura 4. Cau=
dal
observado y el simulado por TOPMODEL y TOPMODEL modificado en calibración.<=
o:p>
=
;
El valor c=
alibrado
de a resultó mucho menor a 0.20,
quizá porque solo los afloramientos rocosos próximos a la red de drenaje
contribuyen a la escorrentía rápida. Afloramientos ubicados a lo sumo a 44 =
m de
la red de drenaje constituyen un 25% del área de afloramientos, de acuerdo =
con
el cálculo de las distancias entre los diferentes elementos topográficos y =
la
red de drenaje hecho con ILWI 2 .
Por lo tanto, si consideramos que la precipitación se distribuye de forma
uniforme en la zona de estudio, un 5% de ella caería sobre los afloramientos
ubicados a lo sumo a 44 m de la red de drenaje, porcentaje de flujo que se
redireccionó en la versión mostrada de TOPMODEL modificado. Sin embargo, ot=
ros
factores podrían explicar el bajo valor de a ,
como la presencia de fracturas en los afloramientos y el efecto de la fuerte
evapotranspiración.
Se determi=
naron
los límites de incertidumbre del 95% para TOPMODEL y TOPMODEL modificado,
descartando los conjuntos de parámetros con eficiencia menor a 0.3. Más que
comparar la estrechez de los límites, se notó que el caudal observado se
encuentra fuera de los límites por más tiempo en el caso de TOPMODEL que en=
el
caso de TOPMODEL modificado. Se calcularon los límites del 95% y no los de =
90%,
ya que es más fácil apreciar que el caudal observado y el límite inferior d=
e TOPMODEL modificado coinciden =
la mayor
parte del tiempo. Según este criterio TOPMODEL modificado es una mejor
representación.
Figura 5. C=
audal
observado y el simulado por TOPMODEL y TOPMODEL modificado en validación.
La validación de los modelos se llevó a =
cabo usando los parámetros obtenidos de sus mejores
calibraciones y las series de precipitación y evapotranspiración del=
01/09/2012 al 31/03/2013. La Figura 5 muestra =
el
caudal observado y el simulado por TOPMODEL y TOPMODEL modificado en
validación. La eficiencia obtenida por TOPMODEL=
fue
de 0.72 y la obtenida por TOPMODEL modificado de 0.76, eficiencias mejores o
iguales a las obtenidas en calibración respectivamente. TOPMODEL modificado
obtiene solo una pequeña ventaja quizá por tratarse de un año más seco con =
un
porcentaje de datos interpolados; sin embargo, imita mejor la dinámica que =
su
contraparte, que genera curvas de recesión generalmente más suaves.
4. CONCLUSIONES
Se modificó TOPMODEL buscando representa=
r el
comportamiento hidrológico de los afloramientos rocosos presentes en cuenca=
s de
páramo andino venezolano, dicha modificación se llevó a cabo considerando el
conocimiento obtenido en investigaciones previas. El TOPMODEL modificado pa=
rece
representar mejor la dinámica que TOPMODEL, mejoró los picos y las curvas de
recesión, obteniendo eficiencias Nash-Sutcliffe superiores tanto en calibra=
ción
como en validación. Además, logra contener la descarga observada dentro de
límites de incertidumbre del 95% por más tiempo. Asumiendo un coeficiente de
escorrentía de 1 en los afloramientos y de acuerdo con la calibración, la
lluvia que cae en un 25% del área de afloramientos es redireccionada a
escorrentía superficial, posiblemente se trate del conjunto de afloramientos
ubicados a lo sumo a 44 m de la red de drenaje. Sin embargo, otras
interpretaciones son posibles ya que otros factores podrían explicar el bajo
valor de a , como la presencia de
fracturas y el efecto de la fuerte evapotranspiración. Por lo tanto, sería
conveniente realizar más estudios sobre la respuesta hidrológica de los
afloramientos rocosos presentes en el área de estudio a diferentes escalas;=
así
como también la evaluación de diferentes hipótesis mediante el uso de model=
os.
Por ot=
ro lado,
la mayoría de los valores calibrados de los
parámetros, tanto=
para el
caso de TOPMODEL como de TOPMODEL modificado , pertenecen a un rango con significado físico. Algunos ajustes
debieron hacerse en un par de parámetros en función de las características
particulares del páramo andino venezolano. Destaca el comportamiento de vr que parece estar revelando
deficiencias de los modelos para la representación. Otros aspectos que requieren de una eval=
uación
es el uso del modelo Green y Ampt en la determi=
nación
del flujo para infiltración y la presunción de estado estacionario d=
e la
zona saturada, sobre la que se fundamenta TOPMODEL.
&=
nbsp;
&=
nbsp;
REFERENCIAS
<=
span
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TOPMODEL requiere la altura del agua de lluvia,=
de
evapotranspiración y caudal en m por paso de tiempo. Los datos de lluvia y
evapotranspiración fueron convertidos de mm a m. Los datos de caudal fueron
convertidos de m3 /s a m3 /10 min multiplicando por 600
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en m2 ,
para obtener el caudal en m/10 min.
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//////////////////////////////////////////////////////////////////8AAAAAAP//
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/////////////7a2ttvb////29vb2///2////////9vb27bbtra2kNvb25C22/+2kLbb////29vb
2///2////9v//7aQttv/25Db/9uQZtvb2///25C22///29vb/7bb2///29vb/9vbtv//2///////
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////////////////////////////////////////////////////////////////////////////
/////////////////9v//7a22//b2///////////////////////////////////////////////
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////////////////////////////////////////////////////////////////////////////
/////////////////////////////////////wAAAAAA////AAAA////////////////////////
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////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////2///trbbkLbbZpCQtmaQ29vb27bb
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///////////////////////b2//b29vb27bb29v//9vb2//b/9vb29vb29u227bb27bb/9vbtrbb
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//////////////////////////////////////////////////////8AAAAAAP///wAAAP//////
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/////////////////////////wAAAAAA////AAAA////////////////////////////////////
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////////////////////////////////////2///trbbkLbbZpCQtmZm2//btrbb27a2kJC22/+2
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////////////////////////////////////////////////////////////////////////AAAA
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////////////////////////////////////////////////////////////////////////////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////////////////////////////////////////////////////////////AAAAAAD///8AAAD/
////////////////////////////////////////////////////////////////////////////
//////+QkNv//7b///////////////////////+QkLZmZpDbtpC2trbbtraQkLZmkJC2kJCQttuQ
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////////////////////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////////b///b
29vbtrb//9v////b29u227bb/9vbtrbb29vb27bb29vb27b//9vb29vb27b//9v////b29vb29vb
27bb27b//9vb29u229v//9v///+Q2//bkGbb/9u2kLbb/9vb29vbtrbb29vb27aQ29v/tpDb29u2
tpD//9vb29vb/9vb29v/29v///+2tra229vb27b/29vb29vb27bb27b//9v////b2//b29vb27b/
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//////////////////////////////8AAAAAAP///wAAAP//////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
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////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
/wAAAAAA////AAAA////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////AAAAAAD///8AAAD/////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
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////////////////////////////////////////////////////////////////////////////
//////////////////8AAAAAAP///wAAAP//////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
/////////////////////////////////////////////////////////////////wAAAAAA////
AAAA////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
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////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////AAAAAAD///8AAAD/////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
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////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
//////8AAAAAAP///wAAAP//////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
/////////////////////////////////////////////////////wAAAAAA////AAAA////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////AAAAAAD///8AAAD/////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////8AAAAA
AP///wAAAP//////////////////////////////////////////////////////////////////
/////////////////wAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAP//////////////
///////////////////////////////////////////////////////b2///////////////////
/////////////////////////////////////////////////////////9v//7a22/+2tv//////
/////////////////////////////9v//9u22//////////////////////////////b2///////
/////////////////9vb2////////////////////////////9v//9u22///////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
/////////////////////////////////////////wAAAAAA////AAAA////////////////////
////////////////////////////////////////////////////////////////kJC2tra2tra2
tra2//+2kLbbkLaQkLbbtpCQkLbbtmaQ///b////ttv/traQtrbbtrZm////kNvbkLaQ27a2tra2
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////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////AAAAAAD///8AAAD/////////////////////////////////////////////////
//////////////////////////////////+Qtrbb29u229vb27bb29vb29vb29vb29vb27aQ29vb
kGbb/9v///+Q2/+2kGa2ttuQtmbbtraQkLaQ29vbtpC2tra2ttu2tma2ttuQtmaQkJD////////b
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29vb29v//9v///+22///27bb29v//9uQ2//bkGbb27bb27b//9vb29v//9vbttvb27bb27bb27bb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////////////////////////////////////////////////////////////////////////////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////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
/////////////////wAAAAAA////AAAA////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////29vb27bb////////////////////////////29vb////////////////////////////
////////////////////////////////////////////////////////////////////2///27bb
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////2///trbb/9vb////////////////////////////////////////////////////
/////////////////////////////////////9vb////////////////////////////////////
////2///27bb////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////AAAAAAD///8A
AAD/////////////////////////////////////////////////////////////////////////
///////b//+2traQtraQtra2kJC2traQtra2tra2traQtraQtrb/trbb//+2trbb29u2ttu2kLa2
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//////////////////////////////////8AAAAAAP///wAAAP//////////////////////////
/////////////////////////////////////////////////////////9vb29vbtpDb29u2kNvb
29vbtrbb29u2kNvb25Db2/+2kP///9vb2///29vb/9vbttvbtrb/27aQtrbbttvb2//b29v//7a2
tv///9v//9vb29v/27a2traQttvbtv//29vb27bbttu2kP///9vb/5CQkP//27bb/9vbttvb29u2
ttvb/9vbttvb29vbtv//29vb29vbttvb/9vb2///27bb29u2kNvb25Db2/+2kLbb29u2kNvb29vb
29vb2///27bb29u2kP///5C225CQkP/bttvb29vb2///25CQttvbttvb29vbttvb29v/27a2traQ
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29vbttv/27bb29u2kNvb29vbttvbtv//29vb27bbttu2kLbb29u2kNv//9vb/9vbttvbtv//2///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//////////////////////8AAAAAAP///wAAAP//////////////////////////////////////
/////////////////////////////////////////////9vb/9vb29vbtpCQkJCQkNv/29vb/9v/
29vb27bbttu2kP///////9vb/5CQkP//29vb////2////9v//9vb29v/27a2traQtv//29vb2///
27bb/9vbttvb29u2ttvb/9vbttvb29vbtv//29vb2///29vb29vbtv//25Db//+2kNvb2///29vb
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ttvbtrb//7aQttvbtrbbttu2kNv//9vb/9vbtv//29v//7a2traQttvbtv//2////9vb29vbtrbb
tv//25CQttvbtra2kNv//7a2traQtv//27bb29u2kP///5CQttvbtra2kNvb2///29vb////29vb
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/////////////////////////////////////////////////////////////////////wAAAAAA
////AAAA////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////AAAAAAD///8AAAD/////////////////////
////////////////////////////////////////////////////////////////////////////
///////////////////////////////////////////b///bttv/////////////////////////
////////////////////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////b29v/////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
///////////////////////////////b///bttv/////////////////////////////////////
///////////////////////////b//+2ttv/29v/////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
//////////8AAAAAAP///wAAAP//////////////////////////////////////////////////
/////////////////////////////////7bb25C2tpC2tv+2ttv//7a2tra229vb22aQ25CQZv+2
tv///7bb25C2tpCQtpCQZraQkLa22//b25C225C2ZpC2kJCQtpCQZpC2kNu2ttu2tv///7bb25C2
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/////////////////////////////////////////////////////////wAAAAAA////AAAA////
////////////////////////////////////////////////////////////////////////////
////29vb29vbkNvb/7aQ2///27a229v////b29vbvNu2tra8/9vb2///29vb29vb29u229u229vb
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////////////////////////////AAAAAAD///8AAAD/////////////////////////////////
///////////////////////////////////////////////b//+2traQtraQtra2kJC2traQtra2
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//////////////////////////////////////////////////////////////////////////8A
AAAAAP///wAAAP//////////////////////////////////////////////////////////////
/////////////////////9vb29vbtpDb29u2kNvb29vbtrbb29u2kNv//9vb29vb29v/29u2ttvb
////29vb/9v/29vb29u2ttvbttvbttvb29vbtpDb2/+2kJCQttvbtrbb/9vbttvb2///29vb2///
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/////////////////////////////////////////////wAAAAAA////AAAA////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////AAAAAAD///8AAAD/////////////////////////////////////////////
//////////////////////////////////////////+229vbttv////////b//+2ttv/29v/////
///////////////////////////////////////b29v/////////////////////////////////
///////////////b29v/////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
///////////////////b29v/////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////////b///b
ttv/////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////8AAAAAAP///wAA
AP//////////////////////////////////////////////////////////////////////////
/////9v//9u2tpC227a2Ztvb27a2tv//27a2ttvb25C2tma2kJBmZra2kGaQ27aQZpC2tpC2tv+2
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/////////////////////////////////wAAAAAA////AAAA////////////////////////////
////////////////////////////////////////////////////2///tra229vb27a2///b29vb
///b29v////b29vb29u229u229u2ttu227aQ29vbkNvb/7aQ2///kJC229u2/9vb2///tra2tpC2
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////////////////////////////////////////////////////////////////////////////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25C227aQkGaQ29uQZrbb25C2trZmZv/b27a2trbb27a225CQtra2kNv//7a22//b25C2tra2tpC2
tv+2tpCQtv//2///////////////////////////////////////////////////////////////
/////////////////////wAAAAAA////AAAA////////////////////////////////////////
////////////////////////////////////////2///kJC229u2/9vbkNv/25Bm29vb29u229v/
29vb///bttv/29u2///b29vb29vb///bttvbttvb29u2/9vbkLa227aQ2///29v/29u2///b////
29v/kJCQ///b2///tra2tpC2///b29vb///bttv/29u2tra2trbbkLZmZjpmkNvb27aQtra2trbb
trZmtrbbkLZm29vbtra2////////29vb29u2///b29vb29vb2//bkJC2ttvb///b29vbkLaQ29vb
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2///kJC229u2/9vb////2///29vb29vb29vb29u229u2///b29v/29u2ttu227aQ2///29vb29vb
///bkJC229u2ttv/29u229vb///b29v////bZpC2traQtpC2///bttvb///b////////////////
////////////////////////////////////////////////////////////////////AAAAAAD/
//8AAAD/////////////////////////////////////////////////////////////////////
///////////////////b29v////////////////////b//+2ttv/29v////////b///bttv/////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
///////////////////////b///bttv/////////////////////////////////////////////
///b29v/////////////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////////b29v/
///////////////////////////////////////////////////////////b///bttv/////////
////////////////////////////////////////////////////////////////////////////
//////////////////////////////////////8AAAAAAP///wAAAP//////////////////////
/////////////////////////////////////////////////////////9v//5C2trZmkNv/tma2
27aQZra227a2tra227aQkNvb27aQtv///9v//5C2traQkLa229vb27a227a2tra2tpC2tra2kLa2
tv//29v//7a227aQkNv//7a2tpC2tv+2tpCQtv//2////5C225C2tpCQkNu2tra2tra227a2ttv/
22aQ27aQZpC2tpCQtv/bttv//2aQ27aQZra2tv//29v//2a2tpBmkNuQkNv//7a2tra2ttv/25C2
traQkLa2tpC2tpC2kJC2kNu2tra2tpC2tpC2tv+2ttv//5C2traQtv//ttv//7a2tma2trZmZv//
2////7bb/7a2kLa22///tra2tpDb25C2kNu2tra2tra227a2Zra225CQZpCQZtvb2////////9vb
/9v/25C2ttuQkLa22///27a229v/27a2tma2tpBmkLZmkP//ttv//5CQ27a2kJC2tpCQtpCQZpC2
ttu2tra2tra22//b2////7bb25C2tpCQtpCQZraQkLa227aQttv/tra2ttv/27a2tma2trZmZv//
2///////////////////////////////////////////////////////////////////////////
/////////wAAAAAA////AAAA////////////////////////////////////////////////////
////////////////////////////2///kJC229u2/9vbkNv/25Bm29vb29u229v/29vb///bttv/
///b////29vb29u229vb///b29v/29u229u229u229u229u2///b////29v/kJCQ2//btra2tpC2
///bttvb///b////29vbttvb29u2/9vb29vb29vb29u2///b29vb29u229u229u2///b////29vb
29u229u2///b////29vbttvb27aQ////29vb29u2///b29vb29u229u229u229u229u22//b27a2
29vbkNvb/7aQ2///kJC229u2/9vb2///tra2tpC229u2///b////kNv/tpBmtrbb//+2kLa2Zjpm
kNvb27aQtra2trbbtrZmtrbbkLZmkJCQ////////////ttv/29u2tpC22//b29vb///b29vb2//b
tra229vbZrbb25Bm/9vb////29vb2//b29vb29vb29u2kNvb27aQ27a229v////b////2///29vb
29vb29u229u2ttvb29u2/9vb29vb2//btra2tpC229u2///b////////////////////////////
////////////////////////////////////////////////////////AAAAAAD///8AAAD/////
////////////////////////////////////////////////////////////////////////////
///////////////////////////////////////////b29v/////////////////////////////
///b///bttv/////////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////b///bttv/
////////////////////////////////////////////////////////////////////////////
///////b//+2ttv/29v////////////////////b///bttv////////////////b//+2ttv/29v/
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
//////////////////////////8AAAAAAP///wAAAP//////////////////////////////////
/////////////////////////////////////////////////9vb/9v/22a2trZmZtv/27a2tra2
29vb27a225CQtra2kP//ttv//5C225CQkLa2trZmkLb//5BmkNvb27a2traQtv//29v//2aQkP+2
ttv//7a2tma2trZmZv//27bb/9u2tpC2tpC2kNu2tra2tpC2tpC2kNu2tpC2tmZmkNvbtpC2tv+2
tra22522tma2tpBmkNu2tpC2tmaQtpCQZv+2ttv//5C2tmZmtraQZmaQ25CQZpCQtraQkP/b29v/
/7a225C225CQkP+2tpC227a2kJCQkJC2ttu2tra2tra2ttv/25CQ2//btpC2tpCQkLa2ttvb25C2
tpCQtpCQkLaQkLa2ttvb22a2trZmkLa2tra227aQkNvb25CQtpCQ2//btrbb25C2ttu2tpC2traQ
kNu2tv///5C227a2kJDb22ZmZv+2ttv//5CQ29vbtra225C225CQkP+2tra227bbtma225BmZra2
kGaQ25CQZtvb25CQkNv/22aQ27aQZpC2tpCQtv/btv///9vb/9v/22a2trZmZv//2///////////
/////////////////////////////////////////////////////////////////////////wAA
AAAA////AAAA////////////////////////////////////////////////////////////////
////////////////////ttv/29u2tpC229u2///b29vb29vb///bttv/kLaQ27a2/9vb////ttv/
29u229vbtpC2///btrbb//+229vb29u2///b////ttvb///b2///tra2tpC229u2///btrbb29vb
29u829u2///b29vbkNu227a2/9vb29vbtraQ///b29vb///bttv//9u229vbkNvb/7aQ29vb29u2
29u2///b////29vb27a229u229u229u229vb29vb///b////29v/29vb29u2///bttvbtraQkLa2
29vb29vb27a229vb///b29vb///b29v/29u229vb///b29vb29vb29vb29u229u22//btpC229vb
29u229v/29vb///bttv/29u2///bttvb29vb/9vb29vbtv/b27a22///29vb29vbtv/bkDpm///b
////29vb///b29v/29vb29u2///b29vb2//bkNv/25Bm29u2ttu2tpCQ///btra2///b29vb29u2
29u229u2///b////ttv/29u2tpC229u2///b////////////////////////////////////////
////////////////////////////////////////////AAAAAAD///8AAAD/////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
//////////////8AAAAAAP///wAAAP//////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
/////////////////////////////////////////////////////////////wAAAAAA////AAAA
////////////////////////////////////////////////////////////////////////////
////////trbbkJCQOpCQOmY627Zmttv//9u2ZpC2kGZmtra2ZpCQtpCQ29vbttv//9u2////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////AAAAAAD///8AAAD/////////////////////////////
//////////////////////////////////////////////////////+Q2///tpA6kLYAADr/27a2
ttvbtraQkLaQkJCQ29v/tpC2trbb29u2trbbtrb/////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
//8AAAAAAP///wAAAP//////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
/////////////////////////////////////////////////wAAAAAA////AAAA////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////AAAAAAD///8AAAD/////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////8AAAAAAP//
/wAAAP//////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
/////////////////////////////////////wAAAAAA////AAAA////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////AAAAAAD///8AAAD/////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////8AAAAAAP///wAAAP//////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
/////////////////////////wAAAAAA////AAAA////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////AAAA
AAD///8AAAD/////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
//////////////////////////////////////////8AAAAAAP///wAAAP//////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
///////////////////////////////////////////b2///////////////////////////////
///////////////////////////////////////////////////////////b29v//9u22///////
///////////////////////////////////////////////////////b2///////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
/////////////wAAAAAA////AAAA////////////////////////////////////////////////
////////////////////////////////////kLa2kJDb29u2Oma2kJBm29vbtra2kJDbtpCQ2//b
27bbttvbkJDbkJCQtrZm///b////29v/2//btra2trbbtrZmkNvbkLaQ27a2tra2trbbtrZmtrbb
kJBm29u2tra229vb2///kLa2kJC2kJCQZpC2tmZm2//bOma2kJCQ27a2trbb29vbZrbbtmZm2//b
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tra2trbbtpC22//btra2kLbbtpC2trbb/9vbkLbbtra2tpC2///b////////////////////////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29u2ttv/29uQtttmtpCQZmaQkLa2kJD/29vb//+QkNvb27ZmttuQkGbb25CQtra2kLbb27aQttvb
tra2trbb/9tmZrbb27a2traQtraQtrb/trbb//9mttu2Zmbb/9tmttu2kGaQtraQtpDbtraQkNu2
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kJC2traQkNu2kJD//9u229tmtra2kGaQtra2tpC2trbb29u2traQtra2tpBmkNvbkJC229uQtttm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kNvb29vbttvbtv//29vb27bbttu2kNvb29vb29v/29vb/9vbttvbttvbtv//29vb29vb2///29vb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tra2kGa2trb//9uQttu2tpDb/9uQtrZmOpC227aQZmbb/9uQttvbtra2trbb27b/////////////
//////////////////////////////////////////////////////////////////////8AAAAA
AP///wAAAP//////////////////////////////////////////////////////////////////
/////////////////9vb27bb29vbttu2tv//29vb25Db29uQkP//29vb/9vb2///29vb2///29vb
29vb2///29vb/9vbtrbbtpCQtv//29vb29vbttvb25Db2///29vb2///2////7a2tv//2////5C2
trbb29u2tv/b27bb2///29vb/9v/29vb29u2tv//29vb/9vbttvbtv//29vb2///29vb29v/29vb
29u2tv//27bb///btpC227aQttvbtv///5Db//+2kNvb29vbttu22///27a2tv//ttvb2///25Db
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29vbtv//29vb29vbtpDb29u2kNvb29vbttvb29vb29v/29vb/9vbttvbtv//25Db/9uQZv//29vb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29vb27a2tpC2kLaQtrbb25C2tpC2kNu2tra2tra2ttv/22a227ZmZtv/27a2tv//25C227a2tpC2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29u229u229u229vb2//b29vbttu227aQ29v/29u22//b29vb/9vb////kNv/25Bm///b////////
////////////////////////////////////////////////////////////////////////////
AAAAAAD///8AAAD/////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
///////////////////////////////////b///bttv/////////////////////////////////
////////////////////////////////////////////////////////////////////29v/////
///////////b////29v////////////////////////////////b////29v/////////////////
///////////////////////b////29v/////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////8AAAAAAP///wAAAP//////////////
/////////////////////////////////////////////////////////////////////5C225C2
tpCQkNvb27a2tra2ttv/25CQtv/b27a229v/25CQ25CQZpCQttvb27a2tmaQ25CQZraQtra2kJC2
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kLa2ttv/27a2ttvb22aQ27aQZmaQ25CQZpCQtpCQZra2kLa2tra22//b25C2tma2trZmZtv/27a2
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29v//5C222aQkJBmkNu2tpC2traQkLa229vb25CQ29vbtma2tpBmZtu2tmaQ25CQZpCQtraQZrbb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29v////b29vb2//b29vb27a2///b29vb29u229vb29u2///b29v////btra2//+2kNv//7aQ29vb
29u229vb///b29vbkJCQ2//b29v/ttu2///b29vb29vb2//b29vb///bkJC229vb29u2ttu2tpCQ
2//btpC22//bttvb25CQ29v/29u2ZpC2kJCQ29u2///b29vb29u2///b////////////////////
////////////////////////////////////////////////////////////////AAAAAAD///8A
AAD/////////////////////////////////////////////////////////////////////////
///////////////////////////////////b//+2ttv/29v/////////////////////////////
29v////////////b///bttv/////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////b///bttv/
////////////////////////////////////////////////////////////////////////////
///////////////////b////29v////////////b///bttv/////////////////////////////
////////////////////////////////////////////////////////////////////////////
///////b///bttv////////////b///bttv////////////////////////////////////b////
29v/////////////////////////////////////////////////////////////////////////
//////////////////////////////////8AAAAAAP///wAAAP//////////////////////////
/////////////////////////////////////////////////////////7bb25C2tpBmkLa2Zra2
ttv/27aQkJC2tmZmttuQkNv//5CQttvb22a2trZmZra2tv//29v//2a2tpBmZtu2tra2ttvb22aQ
27aQZmaQ25CQZpCQtpCQZra2kLa2tra229vb27a22//btv///5C2tma2trZmZv//27bb22a2traQ
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////////////////////////////////////////////////////////////////////////////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kP/bkJC222aQtmaQkLZmkP/b29v//5C2tpC2kP+2ttv//7a2ttvbttv//2aQ22aQZpA6kP/btra2
tra229vbtra229v/25C229u2tra2tv//25C225CQkNvbtra2tmZmtraQkP//2///////////////
/////////////////////////////////////////////////////////////////////wAAAAAA
////AAAA////////////////////////////////////////////////////////////////////
////////////////29vb29vb29u2kNvb27aQ29vb29u22//btpCQ///b////29vb29vb///b////
ttvb///b29v/29vb29u229u2///b29v/29u229u229vb2//bttv/29u2///b////kNv//7aQ29vb
///bkJC2ttu229vb/9vb29v////b////kNv/25Bm///b////29vbttu227aQ29vb///b2///27a2
ttvb///b29v////b////29v/29u229u2///b29vb29u229u2kNvb25CQ///b////29vb///b29v/
29u2///b////29vb29u2////27bb29u229u229u2///bZpC229u2/9vb29vbttu227aQ29vb///b
////trbb//+229v/29vb29u229u2///b////////kLa2kJCQ///b29vb29u2kNvb25CQ///b////
29vb29u2///b////29vb29u2////29vb29u227a2///bttvb29vb2//b29vb///bkNv//7aQ29vb
2//b29vb27a2///b29vbttu229u2///b////////////////////////////////////////////
////////////////////////////////////////AAAAAAD///8AAAD/////////////////////
////////////////////////////////////////////////////////////////////////////
///////b///bttv////////////////////////b////29v/////////////////////////////
///b////29v/////////////////////////////////////////////////////////////////
///////////////////////////////////////////////b//+2ttv/29v/////////////////
////////////////////////////////////////////////////////////////////////29v/
///////b///bttv/////////////////////////////////////////////////////////////
///////////////////////////////b///bttv/////////////////////////////////////
///////////b////29v////////////////b///bttv/////////////////////////////////
29v/////////////////////////////////////////////////////////////////////////
//////////8AAAAAAP///wAAAP//////////////////////////////////////////////////
/////////////////////////////9v//7a2tpC2tpBmkLa2kP/b29v//7a2ttvb25C229uQkNv/
/5C225CQkNvb25CQkNv/27aQkJC227a2kP/b29v//5C2tpCQtraQZrbbtpC227aQkGaQ29uQZv//
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22aQkLa222aQ25CQZpCQtraQZtv/22a2traQZra2tv//27bb25CQ29vbtma227ZmZv//25C227a2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2//bttv//2a2tpBmZraQkGa225A6kNvbtpC22/+2tv///5C2tpCQkJC2tpCQkJCQtraQkNvb29u2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kGbb29u2tra2trbb/9tmttu2Zmb//9uQ29u2trbbttv//9uQtv//27b/////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////8AAAAAAP//
/wAAAP//////////////////////////////////////////////////////////////////////
/////////////5C2ttu2tv//27bb/7aQkNvbtv//25Db/9uQZv//29vb29vbttvb29vbtv//29vb
29vb29v/27bb/9vbtv//29v//9vb////27a22///25Db/9uQZv//29v//9vb29u2trbb////2///
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//+2kNvb2///29vb29vbttvbttv/29u2trbb29vbtrbb27aQkP//29vb29vbtv//25Db/9uQZv//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kLaQ27a2tra2kLa2kLaQ27a2kLa2ZmaQ/9u2////////////////////////////////////////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kGZm///btrbb///bkLa2tra2tra2ttu2Zra2tmaQ/9vbtra2ttvbkLaQ27a2ZpC227a2trbb/9vb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tra229u229v/2//bZpDbtpCQkLa2/7a2kNvbZjqQ/9u22///kNvbOjpmkJBm/7a22///tra229vb
tpCQkLbbtraQkLbbkJCQ29vbkJDb27aQ////ttv/27a2kLa2ZraQtmZmtra22//bZra2tmZmttu2
kJDb/9u2////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////AAAAAAD///8AAAD/////////////////////////
///////////////////////////////////////////////////////////bttv///+2trb///+2
29u2kJDb29v//9u2trbb/7a2kLb//9vb29u229v//9v///+Q2//bkGb//9uQtra2kJDb29vb/9vb
tra22//btpDb///b29vb29v//9vb29v//9u2trbb2//b27a2/9vb29vbtrbb27bb27bb/9uQ2//b
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