Cressman: Cressman Objective Analysis Method
In InterpolateR: A Comprehensive Toolkit for Fast and Efficient Spatial Interpolation
Cressman R Documentation
Cressman Objective Analysis Method
Description
The Cressman objective analysis computes values at grid points Z_{ij}^a (where i and j are the grid point indices for a 2D grid)
as the weighted average of the difference between observed values Z_k^o and background values interpolated to the
observation locations Z_k^b (i.e., Z_k^o - Z_k^b, called the observation increment) plus the background value
at the grid point Z_{ij}^b.
Usage
Cressman(
BD_Obs,
BD_Coord,
shapefile,
grid_resolution,
search_radius,
training = 1,
n_round = NULL,
stat_validation = NULL,
Rain_threshold = NULL,
save_model = FALSE
)
Arguments
BD_Obs
A data.table or data.frame containing observational data with the following structure:
The first column (Date): A Date object representing the observation date.
The remaining columns: Each column corresponds to a unique ground station, where the column name is the station identifier.
The dataset should be structured as follows:
> BD_Obs
# A data.table or data.frame with n rows (dates) and m+1 columns (stations + Date)
Date ST001 ST002 ST003 ST004 ...
<date> <dbl> <dbl> <dbl> <dbl> ...
1 2015-01-01 0 0 0 0 ...
2 2015-01-02 0 0 0 0.2 ...
3 2015-01-03 0.1 0 0 0.1 ...
Each station column contains numeric values representing observed measurements.
The column names (station identifiers) must be unique and match those in BD_Coord$Cod to ensure proper spatial referencing.
BD_Coord
A data.table or data.frame containing the metadata of the ground stations. It must include the following columns:
-
"Cod":
Unique identifier for each ground station.
-
"X":
Latitude of the station in UTM format.
-
"Y":
Longitude of the station in UTM format.
shapefile
A shapefile defining the study area, used to constrain the interpolation to the region of interest.
The shapefile must be of class SpatVector (from the terra package) and should have a UTM coordinate reference system.
grid_resolution
A numeric value indicating the resolution of the interpolation grid in kilometers (km).
search_radius
A numeric vector indicating the search radius in kilometers (km) for the Cressman method.
Note: See the "Notes" section for additional details on how to search radius values.
training
Numerical value between 0 and 1 indicating the proportion of data used for model training. The remaining data are used for validation. Note that if you enter, for example, 0.8 it means that 80 % of the data will be used for training and 20 % for validation.
If you do not want to perform validation, set training = 1. (Default training = 1).
n_round
An integer specifying the number of decimal places to round the interpolated results.
If set to NULL, all decimal places will be preserved. .
stat_validation
A character vector specifying the names of the stations to be used for validation.
This option should only be filled in when it is desired to manually enter the stations used for validation. If this parameter is NULL, and the formation is different from 1, a validation will be performed using random stations.
The vector must contain the names of the stations selected by the user for validation.
For example, stat_validation = c(“ST001”, “ST002”). (Default stat_validation = NULL).
Rain_threshold
List of numerical vectors defining precipitation thresholds to classify precipitation into different categories according to its intensity.
This parameter should be entered only when the validation is to include categorical metrics such as Critical Success Index (CSI), Probability of Detection (POD), False Alarm Rate (FAR), etc.
Each list item should represent a category, with the category name as the list item name and a numeric vector specifying the lower and upper bounds of that category.
Note: See the "Notes" section for additional details on how to define categories, use this parameter for validation, and example configurations.
save_model
Logical value indicating whether the interpolation file should be saved to disk. The default value is FALSE. indicating that the interpolated file should not be saved.
If set to TRUE, be sure to set the working directory beforehand using setwd(path) to specify where the files should be saved.
Value
The return value depends on whether validation has been performed.
-
Without validation: The function returns a list, where each element is a SpatRaster object containing the interpolated values for a specific search radius defined in search_radius. The number of elements in this list matches the length of search_radius.
-
With validation: The function returns a named list with two elements:
-
Ensamble: A list where each element corresponds to a SpatRaster object containing the interpolated values for a specific search radius in search_radius.
-
Validation: A list where each element is a data.table containing the validation results for the corresponding interpolated SpatRaster. Each data.table incluye métricas de bondad de ajuste como RMSE, MAE y Kling-Gupta Efficiency (KGE), junto con métricas categóricas si se proporciona Rain_threshold.
The number of elements in both the Ensamble and Validation lists matches the length of search_radius, ensuring that each interpolation result has an associated validation dataset.
Details
The Cressman method is defined by the following equation:
Z_{ij}^a = Z_{ij}^b + \frac{\sum_{k=1}^{n} w_k (Z_k^o - Z_k^b)}{\sum_{k=1}^{n} w_k}
where:
Z_{ij}^ais the analysis value at grid point i,j.
Z_{ij}^bis the background value at grid point i,j.
Z_k^ois the observed value at station k.
Z_k^bis the background value interpolated to station k.
w_kis the weight assigned to station k.
nis the total number of stations used.
The weight w_k is a function of the distance r = \sqrt{(x_{ij} - x_k)^2 + (y_{ij} - y_k)^2}
between the individual observation k and grid point (i, j). R is the influence radius.
Beyond the influence radius, the weight is set to zero. R is therefore often referred to as
the cut-off radius.
Note
The search_radius parameter defines the influence range for the Cressman interpolation method.
It determines the maximum distance (in kilometers) within which observational data points contribute
to the interpolated value at a given location. A larger radius results in smoother interpolated fields
but may oversmooth local variations, while a smaller radius preserves finer details but may introduce noise.
The Cressman method typically applies an iterative approach, where the search radius is progressively reduced
to refine the interpolation. Each iteration recalculates interpolated values with a smaller radius,
allowing a better representation of small-scale features in the dataset.
The search_radius should be defined as a numeric vector representing the influence range in kilometers (km)
for each interpolation iteration. For example, setting search_radius = c(50, 20, 10) means the first iteration
considers a 50 km influence radius, the second iteration uses 20 km, and the final iteration refines
the interpolation with a 10 km radius. The number of elements in search_radius determines the total number of iterations.
The Rain_threshold parameter is used to calculate categorical metrics such as the Critical Success Index (CSI),
Probability of Detection (POD), False Alarm Rate (FAR), success ratio (SR), Hit BIAS (HB),Heidke Skill Score (HSS);
Hanssen-Kuipers Discriminant (HK); Equal Threat Score (ETS) or Gilbert Skill Score.
The parameter should be entered as a named list, where each item represents a category and the name of the item is the category name.
The elements of each category must be a numeric vector with two values: the lower and upper limits of the category.
For example:
Rain_threshold = list(
no_rain = c(0, 1),
light_rain = c(1, 5),
moderate_rain = c(5, 20),
heavy_rain = c(20, 40),
violent_rain = c(40, Inf)
)
Precipitation values will be classified into these categories based on their intensity.
Users can define as many categories as necessary, or just two (e.g., "rain" vs. "no rain").
It is important that these categories are entered according to the study region, as each study region may have its own categories.
Author(s)
Jonnathan Landi jonnathan.landi@outlook.com
References
Cressman, G. P., 1959: An operational objective analysis system. Mon. Wea. Rev., 87, 367-374, doi:10.1175/1520-0493(1959)087%3C0367:AOOAS%3E2.0.CO;2.
Examples
# Load data from on-site observations
data("BD_Obs", package = "InterpolateR")
data("BD_Coord", package = "InterpolateR")
# Load the study area where the interpolation is performed.
shp_path = system.file("extdata", "study_area.shp", package = "InterpolateR")
shapefile = terra::vect(shp_path)
# Perform the interpolation
Interpolated_Cressman <- Cressman(BD_Obs, BD_Coord, shapefile, grid_resolution = 5,
search_radius = 10, training = 1, n_round = 2,
stat_validation = "M001", Rain_threshold = NULL,
save_model = FALSE)
# Results ("Ensamble with 10 km radius")
Radius_10 <- Interpolated_Cressman$Ensamble$`10 km`
# Validation statistics
# Validation results with a 10 km radius
Validation_results_10 = Interpolated_Cressman$Validation$`10 km`
InterpolateR documentation built on Sept. 9, 2025, 5:59 p.m.
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| Cressman | R Documentation |
Cressman Objective Analysis Method
Description
The Cressman objective analysis computes values at grid points Z_{ij}^a (where i and j are the grid point indices for a 2D grid)
as the weighted average of the difference between observed values Z_k^o and background values interpolated to the
observation locations Z_k^b (i.e., Z_k^o - Z_k^b, called the observation increment) plus the background value
at the grid point Z_{ij}^b.
Usage
Cressman(
BD_Obs,
BD_Coord,
shapefile,
grid_resolution,
search_radius,
training = 1,
n_round = NULL,
stat_validation = NULL,
Rain_threshold = NULL,
save_model = FALSE
)
Arguments
BD_Obs |
A
The dataset should be structured as follows: > BD_Obs # A data.table or data.frame with n rows (dates) and m+1 columns (stations + Date) Date ST001 ST002 ST003 ST004 ... <date> <dbl> <dbl> <dbl> <dbl> ... 1 2015-01-01 0 0 0 0 ... 2 2015-01-02 0 0 0 0.2 ... 3 2015-01-03 0.1 0 0 0.1 ...
|
BD_Coord |
A
|
shapefile |
A shapefile defining the study area, used to constrain the interpolation to the region of interest.
The shapefile must be of class |
grid_resolution |
A numeric value indicating the resolution of the interpolation grid in kilometers ( |
search_radius |
A numeric vector indicating the search radius in kilometers ( |
training |
Numerical value between 0 and 1 indicating the proportion of data used for model training. The remaining data are used for validation. Note that if you enter, for example, 0.8 it means that 80 % of the data will be used for training and 20 % for validation. If you do not want to perform validation, set training = 1. (Default training = 1). |
n_round |
An integer specifying the number of decimal places to round the interpolated results.
If set to |
stat_validation |
A character vector specifying the names of the stations to be used for validation. This option should only be filled in when it is desired to manually enter the stations used for validation. If this parameter is NULL, and the formation is different from 1, a validation will be performed using random stations. The vector must contain the names of the stations selected by the user for validation. For example, stat_validation = c(“ST001”, “ST002”). (Default stat_validation = NULL). |
Rain_threshold |
List of numerical vectors defining precipitation thresholds to classify precipitation into different categories according to its intensity. This parameter should be entered only when the validation is to include categorical metrics such as Critical Success Index (CSI), Probability of Detection (POD), False Alarm Rate (FAR), etc. Each list item should represent a category, with the category name as the list item name and a numeric vector specifying the lower and upper bounds of that category. Note: See the "Notes" section for additional details on how to define categories, use this parameter for validation, and example configurations. |
save_model |
Logical value indicating whether the interpolation file should be saved to disk. The default value is |
Value
The return value depends on whether validation has been performed.
-
Without validation: The function returns a
list, where each element is aSpatRasterobject containing the interpolated values for a specific search radius defined insearch_radius. The number of elements in this list matches the length ofsearch_radius. -
With validation: The function returns a named
listwith two elements:-
Ensamble: Alistwhere each element corresponds to aSpatRasterobject containing the interpolated values for a specific search radius insearch_radius. -
Validation: Alistwhere each element is adata.tablecontaining the validation results for the corresponding interpolatedSpatRaster. Eachdata.tableincluye métricas de bondad de ajuste como RMSE, MAE y Kling-Gupta Efficiency (KGE), junto con métricas categóricas si se proporcionaRain_threshold.
-
The number of elements in both the Ensamble and Validation lists matches the length of search_radius, ensuring that each interpolation result has an associated validation dataset.
Details
The Cressman method is defined by the following equation:
Z_{ij}^a = Z_{ij}^b + \frac{\sum_{k=1}^{n} w_k (Z_k^o - Z_k^b)}{\sum_{k=1}^{n} w_k}
where:
Z_{ij}^ais the analysis value at grid point
i,j.Z_{ij}^bis the background value at grid point
i,j.Z_k^ois the observed value at station
k.Z_k^bis the background value interpolated to station
k.w_kis the weight assigned to station
k.nis the total number of stations used.
The weight w_k is a function of the distance r = \sqrt{(x_{ij} - x_k)^2 + (y_{ij} - y_k)^2}
between the individual observation k and grid point (i, j). R is the influence radius.
Beyond the influence radius, the weight is set to zero. R is therefore often referred to as
the cut-off radius.
Note
The search_radius parameter defines the influence range for the Cressman interpolation method.
It determines the maximum distance (in kilometers) within which observational data points contribute
to the interpolated value at a given location. A larger radius results in smoother interpolated fields
but may oversmooth local variations, while a smaller radius preserves finer details but may introduce noise.
The Cressman method typically applies an iterative approach, where the search radius is progressively reduced to refine the interpolation. Each iteration recalculates interpolated values with a smaller radius, allowing a better representation of small-scale features in the dataset.
The search_radius should be defined as a numeric vector representing the influence range in kilometers (km)
for each interpolation iteration. For example, setting search_radius = c(50, 20, 10) means the first iteration
considers a 50 km influence radius, the second iteration uses 20 km, and the final iteration refines
the interpolation with a 10 km radius. The number of elements in search_radius determines the total number of iterations.
The Rain_threshold parameter is used to calculate categorical metrics such as the Critical Success Index (CSI),
Probability of Detection (POD), False Alarm Rate (FAR), success ratio (SR), Hit BIAS (HB),Heidke Skill Score (HSS);
Hanssen-Kuipers Discriminant (HK); Equal Threat Score (ETS) or Gilbert Skill Score.
The parameter should be entered as a named list, where each item represents a category and the name of the item is the category name.
The elements of each category must be a numeric vector with two values: the lower and upper limits of the category.
For example:
Rain_threshold = list(
no_rain = c(0, 1),
light_rain = c(1, 5),
moderate_rain = c(5, 20),
heavy_rain = c(20, 40),
violent_rain = c(40, Inf)
)
Precipitation values will be classified into these categories based on their intensity. Users can define as many categories as necessary, or just two (e.g., "rain" vs. "no rain"). It is important that these categories are entered according to the study region, as each study region may have its own categories.
Author(s)
Jonnathan Landi jonnathan.landi@outlook.com
References
Cressman, G. P., 1959: An operational objective analysis system. Mon. Wea. Rev., 87, 367-374, doi:10.1175/1520-0493(1959)087%3C0367:AOOAS%3E2.0.CO;2.
Examples
# Load data from on-site observations
data("BD_Obs", package = "InterpolateR")
data("BD_Coord", package = "InterpolateR")
# Load the study area where the interpolation is performed.
shp_path = system.file("extdata", "study_area.shp", package = "InterpolateR")
shapefile = terra::vect(shp_path)
# Perform the interpolation
Interpolated_Cressman <- Cressman(BD_Obs, BD_Coord, shapefile, grid_resolution = 5,
search_radius = 10, training = 1, n_round = 2,
stat_validation = "M001", Rain_threshold = NULL,
save_model = FALSE)
# Results ("Ensamble with 10 km radius")
Radius_10 <- Interpolated_Cressman$Ensamble$`10 km`
# Validation statistics
# Validation results with a 10 km radius
Validation_results_10 = Interpolated_Cressman$Validation$`10 km`
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