Informe Final
Juan Pablo Ramírez Rincón
24/6/2020
Itroducción
El siguiente cuaderno es elaborado en Rstudio Para explicar como se realiza una interpolación espacial de usa zona en especifica, Para esto es necesario tener base de datos de nuestra zona de interes, la cual se puede descargar desde la pagina del DANE para datos nacionales.
La interpolación espacial es una parte de la geoestadística que se basa en el cálculo de los valores desconocidos de una variable espacial a partir de otros valores cuyo valor es conocido, de esta manera nos facilita poder tomar como base mapas anteriormente realizados como lo pueden ser de temperatura, precipitación, entre otros. Esto al final nos permite tomar medidas continuas de mediciones puntuales en un territorio.
Tolima
Tolima es un departamento de Colombia el cual posee todos los pisos termicos, desde elevaciones superiores a 5.000 metros de altitud como el Nevado del Huila, hasta valles por debajo de los 400 metros de altitud que alcanzan temperaturas superiores a 40ºC. Este es atravesado de sur a norte por el río Magdalena y posee 3 parques naturales en su territorio los cuales son el parque Los Nevados, Las Hermosas y el Parque Nacional del Nevado del Huila; Su pincipal economía es el cultivo de Café y la ganaderia.
La Lechona y El Tamal
Entre las comidas típicas del Tolima una de la más famosa es la lechona. Un plato a base de carne de cerdo relleno de arvejas, mezclado dentro del mismo lechón. Este se hornea, quedando el dorado y tostado el cuero del lechón. Se sirve con una porción del cuero y ocasionalmente con insulso, una especie de natilla hecha con harina de trigo y un poco de azúcar. Para finalizar el plato de lechona se sirve idealmente en hoja de Bijao, similar a la hoja de plátano, pasada por la llama.
Por otro lado el Tamal Tolimense consiste en una preparación de arvejas secas, carnes de res, gallina, cerdo, huevo, papa, zanahoria y condimentos. El envoltorio de la mezcla se hace con hojas de plátano que además de constituir su característica presentación, también contribuye al sabor del plato. Se acompaña tradicionalmente con chocolate y arepa tolimense. Un dato curioso es que la Alcaldía de Ibague declaro el 24 de Junio día del tamal (hoy).
Datos y métodos
Los datos para realizar el mapa de la distribución de Café en Tolima fueron tomados de DANE.
Para descargar los datos de datos de precipitación global de CHIRPS realizó siguiendo las indicaciones del profesor y con el siguiente enlace, obteniendo los datos de precipitación correspondientes al global_pentad en el directorio tifs, específicamente los datos de los ultimos cuatro días del mes de Marzo de 2020 del Grupo de Riesgos Climáticos de precipitación infrarroja con datos de estación (CHIRPS) y se descomprimió para obtener un archivo tif.
Los Métodos de interpolación utilizados fueron por el método Polígonos de Thiessen los cuales son son una construcción geométrica que permite construir una partición del plano, estos son utiles en distintos campos del conocimiento como lo puede ser epidemiología y meteorología, ya que estos nos ayudan a interpretar datos con mayor facilidad en una área o zona determinada. En general es una herramienta muy buena y basica de los sistemas de información geográfica; Interpolación ponderada de distancia inversa (IDW) esta interpolación estima valores desconocidos al especificar la distancia de búsqueda, los puntos más cercanos, el ajuste de potencia y las barreras para al final obtener un estimado en rango de datos; e Interpolación por método Kriging gracias a este metodo, las técnicas de estadística geográfica no sólo tienen la capacidad de producir una superficie de predicción, sino que también proporcionan alguna medida de certeza o precisión de las predicciones, ya que, presupone que la distancia entre los puntos de muestra reflejan una correlación espacial que puede utilizarse para explicar la variación en la zona de interes.
Resultados
Mapa de Puntos del Departamento de Tolima
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## Geospatial Data Abstraction Library extensions to R successfully loaded
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Interpolación por el método Polígonos de Thiessen
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## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
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## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
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## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
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## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
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## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
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## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
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## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
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## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
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## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
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## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
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## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
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## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
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## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
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## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
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## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
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## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
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## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
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## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
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## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
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## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
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## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
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## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
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## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
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## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
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## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
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## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
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## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
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## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
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## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
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## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
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## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
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## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
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## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
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## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
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## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
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## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
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## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
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## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
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## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
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## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
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## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
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## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
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## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
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## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
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## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
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## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
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## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
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## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
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## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
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## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
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## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
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## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
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## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
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## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
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## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
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## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
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## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
## returning NA
Interpolación Ponderada de Distancia Inversa (IDW)
## [inverse distance weighted interpolation]## class : RasterLayer
## dimensions : 386, 259, 99974 (nrow, ncol, ncell)
## resolution : 700.6245, 700.6245 (x, y)
## extent : 774376.6, 955838.4, 809339.9, 1079781 (xmin, xmax, ymin, ymax)
## crs : +proj=tmerc +lat_0=4.596200416666666 +lon_0=-74.07750791666666 +k=1 +x_0=1000000 +y_0=1000000 +ellps=GRS80 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs
## source : memory
## names : var1.pred
## values : 29.20715, 88.63641 (min, max)## class : SpatialPolygonsDataFrame
## features : 47
## extent : 774500.6, 955884.5, 809390, 1080017 (xmin, xmax, ymin, ymax)
## crs : +proj=tmerc +lat_0=4.596200416666666 +lon_0=-74.07750791666666 +k=1 +x_0=1000000 +y_0=1000000 +ellps=GRS80 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs
## variables : 2
## names : MUNIC, CODIGO
## min values : ALPUJARRA, 73001
## max values : VILLARRICA, 73873## class : RasterLayer
## dimensions : 386, 259, 99974 (nrow, ncol, ncell)
## resolution : 700.6245, 700.6245 (x, y)
## extent : 774376.6, 955838.4, 809339.9, 1079781 (xmin, xmax, ymin, ymax)
## crs : +proj=tmerc +lat_0=4.596200416666666 +lon_0=-74.07750791666666 +k=1 +x_0=1000000 +y_0=1000000 +ellps=GRS80 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs
## source : memory
## names : var1.pred
## values : 29.20715, 88.63641 (min, max)## Warning: The argument auto.palette.mapping is deprecated. Please use midpoint
## for numeric data and stretch.palette for categorical data to control the palette
## mapping.
## class : SpatialPointsDataFrame
## features : 88
## extent : 774500.6, 955884.5, 809390, 1080017 (xmin, xmax, ymin, ymax)
## crs : +proj=tmerc +lat_0=4.596200416666666 +lon_0=-74.07750791666666 +k=1 +x_0=1000000 +y_0=1000000 +ellps=GRS80 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs
## variables : 4
## names : MUNIC, CODIGO, lluvia, rainfall
## min values : ALPUJARRA, 73001, 29.1885028415256, 29.2
## max values : VILLARRICA, 73873, 88.6871142917209, 88.7## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
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## [inverse distance weighted interpolation]Diagrama de Diferencias:
## [1] 9.57424El Diagrama nos arroja un error cuadrático medio (RMSE) de 9.57424 Por esta razón se realiza un mapa de intervalo de confianza del 95% del modelo de interpolación.
## [inverse distance weighted interpolation]## [inverse distance weighted interpolation]
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## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
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Ajuste Polinomial de Primer orden
## Warning: The argument auto.palette.mapping is deprecated. Please use midpoint
## for numeric data and stretch.palette for categorical data to control the palette
## mapping.
Ajuste Polinomial de Segundo orden
## Warning: The argument auto.palette.mapping is deprecated. Please use midpoint
## for numeric data and stretch.palette for categorical data to control the palette
## mapping.
Interpolación por método Kriging
Para la interpolación por método Kriging es necesario crear un modelo de variograma, teniendo en cuenta que el modelo de variograma se calcula sobre los datos de tendencia.
## Warning in fit.variogram(var.smpl, fit.ranges = TRUE, fit.sills = TRUE, : No
## convergence after 200 iterations: try different initial values?## model psill range kappa
## 1 Nug 0.9969201 0.0 0.0
## 2 Mat 2.9369551 144136.9 0.5
Generar superficie Kriged
Se utiliza el modelo de variograma dat.fit para generar una superficie interpolada kriged. La función krige permite incluir el modelo de tendencia, lo que evita tener que reducir la tendencia de los datos, corregir los residuos y luego combinar los dos rásters. Gracias a esto todo lo que hay que hacer es pasar krige la fórmula de tendencia f.1.
## [using universal kriging]## class : RasterLayer
## dimensions : 386, 259, 99974 (nrow, ncol, ncell)
## resolution : 700.6245, 700.6245 (x, y)
## extent : 774376.6, 955838.4, 809339.9, 1079781 (xmin, xmax, ymin, ymax)
## crs : +proj=tmerc +lat_0=4.596200416666666 +lon_0=-74.07750791666666 +k=1 +x_0=1000000 +y_0=1000000 +ellps=GRS80 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs
## source : memory
## names : var1.pred
## values : 36.54305, 76.66296 (min, max)## Warning: The argument auto.palette.mapping is deprecated. Please use midpoint
## for numeric data and stretch.palette for categorical data to control the palette
## mapping.
Una mejor visualización de la interpolación realizada:
Mapas de varianza e intervalo de confianza
Análisis de resultados
Interpolación por el método Polígonos de Thiessen
Para realizar esta interpolación fue necesario reducir los poligonos a 9 veces menos de los previstos en un principio, esto devido a la cantidad de información que muestra el mapa de puntos no se lograba interpretar con facilidad. En este mapa se puede observar según los datos de Precipitación que las zonas norte y sur del mapa son aquellas donde cae más mm de agua, esto quiere decir que hay mayor flujo de lluvia en estas zonas, en cambio en las zonas centrales y del sureste de Tolima son las zonas con menos tendencia a precipitación, con esta información se puede realizar una buena gestión empresarial agronómica en cuanto planeación de cultivos, de este modo se puede decidir con mayor facilidad que cultivos son óptimos en estas zonas.
Interpolación Ponderada de Distancia Inversa
Con esta interpolación nos facilita predecir como se va a comportar una variable en especifico, en este caso es la Precipitación, teniendo en cuenta el mapa se puede observar que las zonas de color blanco son aquellas donde se presenta precipitación median, en cambio como se dijo anteriormente en las zonas norte y sur son aquellas que poseen tendencia a mayor precipitación, en cambio las zonas sureste y un poco central son aquellas que poseen tendencia a sequita o poca precipitación, algo que no se lograba observar con tanta facilidad como por el método de Polígonos de Thiessen.
Para lograr observar que tan confiable es el mapa que se realizó se hizo un diagrama el cual arrojó un error cuadrático medio (RMSE) de 9.57424 Por esta razón se realizó un mapa de intervalo de confianza del 95% del modelo de interpolación. El cual comparado con el anterior que no poseeía el 95% de confianza solo se logra observar que la zona sur de Tolima es la de mayor precipitación en el Departamento comparado a los demas puntos muestrales.
Interpolación por método Kriging
Al momento de realizar el modelo de variograma según los datos obtenidos despues de 200 convergencias no se observan resultados, por esta razón la linea de tendencia esta en el suelo, pero por otra parte se observa que los puntos muestrales tienen una tendencia positiva semi exponencial, lo cual indica en los mapas posteriormente a predecir precipitación en los puntos anteriormente mencionados pero con mayor precisión, siguiendo este orden de ideas las zonas con mayor precipitación es llegando al sur de Tolima y al noreste.
Conclusiones
- Las interpolaciones son muy útiles para muchos campos de la vida cotidiana, como lo puede ser un mapa de trafico, temperatura, tendencias de compras, entre otros.
- Hay que tener en cuenta el Indice de confiabilidad de los datos obtenidos y como estos tienen influencia en la decisión final.
Referencias
Cómo funciona Kriging. (s. f.). www.esri.com. Recuperado 22 de junio de 2020, de https://pro.arcgis.com/es/pro-app/tool-reference/3d-analyst/how-kriging-works.htm#:%7E:text=superficie%20de%20salida.-,%C2%BFQu%C3%A9%20es%20kriging%3F,suavidad%20de%20la%20superficie%20resultante.
Introduction to Spatial Analysis . (s. f.). Introduction to Spatial Analysis. Recuperado 22 de junio de 2020, de http://planet.botany.uwc.ac.za/nisl/GIS/spatial/index.htm
R for Spatial Statistics. (s. f.). gsp.humboldt.edu. Recuperado 22 de junio de 2020, de http://gsp.humboldt.edu/OLM/R/04_01_Variograms.html
University of California, Santa Barbara. (s. f.). CHIRPS: Rainfall Estimates from Rain Gauge and Satellite Observations . Climate Hazards Center. Recuperado 22 de junio de 2020, de https://chc.ucsb.edu/data/chirps