# clim4health downscale

## Overview

This vignette provides an introduction to the `c4h_downscale()` function, used for statistical downscaling of climate data. The different downscaling methodologies are described, and examples of how to use the function are provided. Finally, some considerations for downscaling common variables are discussed.

## 0. Load the package and sample data

First, let’s load the package.

    library(clim4health)

Let’s load some sample data that we can use to demonstrate the downscaling methods.

    fcst_path <- system.file("extdata/forecast/", package = "clim4health")
    fcst_path <- paste0(fcst_path, "/")
    fcst <- c4h_load(fcst_path,
                     variable = "t2m",
                     year = 2025,
                     month = 1,
                     leadtime_month = "all",
                     ext = "nc")

    hcst_path <- system.file("extdata/hindcast/", package = "clim4health")
    hcst_path <- paste0(hcst_path, "/")
    hcst <- c4h_load(hcst_path,
                     variable = "t2m",
                     year = 2010:2012,
                     month = 1,
                     leadtime_month = "all",
                     ext = "nc")

    rean_path <- system.file("extdata/reanalysis/", package = "clim4health")
    rean_path <- paste0(rean_path, "/")
    rean <- c4h_load(rean_path,
                     variable = "t2m",
                     year = 2010:2012,
                     month = 1,
                     leadtime_month = 1:3,
                     ext = "nc")

We can also convert all data to degrees Celsius, as is described in the `clim4health_overview` vignette.

    fcst <- c4h_convert_units(fcst, "celsius")
    hcst <- c4h_convert_units(hcst, "celsius")
    rean <- c4h_convert_units(rean, "celsius")

Look at the dimensions of the observed and hindcast datasets (recall we can use `dim(rean$data)` or `rean$dims`). We can see that `rean` has more latitude and longitude points, despite covering the same area - it has higher spatial resolution. We can also see this by comparing the values of the latitude/longitude coordinates - notice that `rean` has 0.1º resolution, but `hcst` has 1º.

    print(rean$dims)
    print(hcst$dims)

    print(rean$coords$latitude)
    print(hcst$coords$latitude)

We can also plot the datasets to visually confirm the higher spatial resolution.

    # Hindcast data
    c4h_plot(hcst, ensemble = TRUE, coordgrid = TRUE)

    # Observations
    c4h_plot(rean, ensemble = TRUE, coordgrid = TRUE)

We would like to increase the resolution of our forecast and hindcast data, which we will do by using `c4h_downscale()`.

## 1. Key c4h_downscale arguments

`c4h_downscale()` takes a variety of arguments depending on the downscaling to be performed. There are two required inputs for the function.

1. `downscale_function`: a string identifying the method of downscaling to be used.
2. `exp`: an s2dv_cube object containing the experimental data (i.e. a hindcast) to establish the downscaling relationship. If `exp_cor` is not provided, the downscaling will be applied to `exp`.

Additionally, arguments `obs` and `exp_cor` are often required.

3. `obs`: an s2dv_cube object containing the observational data to be used for downscaling.
4. `exp_cor`: an s2dv_cube object of experimental data to downscale. The downscaling will be applied to this data, using the statistical relationship between `obs` and `exp`, if `exp_cor` is provided. For example, you can use the hindcast as `exp` and the forecast as `exp_cor` to obtain a downscaled forecast.

The following figure shows the key arguments for `c4h_downscale()` depending on the downscaling method chosen.

`c4h_downscale()` returns a named list containing two elements, `exp` and `obs`. `exp` is an s2dv_cube object containing the downscaled experimental data (from either `exp` or `exp_cor`), and `obs` is an s2dv_cube object containing the observational data (from `obs`). This looks like:

    forecast_downscaled$
    │
    ├── exp$                    # s2dv_cube object containing the downscaled
    │    │                        experimental data
    │    ├── data                  # Array with named dimensions containing the
    │    │                           downscaled data
    │    ├── dims                  # Named vector of the dimensions of the data
    │    │                           array
    │    ├── coords                # Named list of the coordinates of the data array
    │    └── attrs                 # Named list of all attributes and metadata
    └── obs$                    # s2dv_cube object containing the (potentially
        │                         downscaled) observational data
        ├── data                   # Array with named dimensions containing the
        │                            downscaled observational data
        ├── dims                   # Named vector of the dimensions of the data
        │                            array
        ├── coords                 # Named list of the coordinates of the data array
        └── attrs                  # Named list of all attributes and metadata

> 💡 Note: Often, the output `obs` is the same as the input `obs`. However, this will not always be the case - for example, if you choose to downscale to a sub-region of interest using the argument `bbox`, then `obs` will be cropped to this region as well.

## 2. Downscaling methods (gridded data)

The downscaling methods available through clim4health are a simple interpolation, an interpolation plus bias correction (Intbc), an interpolation plus linear regression (Intlr), or the analogs method. Let’s explore the different downscaling options.

### Method 1: Interpolation

This is the simplest method of downscaling available through clim4health. It involves a regrid of coarse-scale gridded climate data onto a finer-scale grid, or a similar interpolation of gridded model data to a point location.

> 💡 Note: Other downscaling methods, Intbc and Intlr, involve this method as a first step. These methods are explained below.

Different interpolation methods, based on different mathematical approaches, can be applied: conservative, nearest neighbour, bilinear or bicubic. This method does not rely on any data for training (i.e. no observations are used to adjust the forecast data).

- First-order conservative regridding preserves the integral of the source field across grids.

- A nearest neighbour regridding considers the values of the nearest neighbours on the source grid, possibly weighted by their distance to the target point, and associates these to each target grid point.

- The bilinear approach uses a linear interpolation in two directions considering the four nearest grid cells of original data.

- Similarly, bicubic interpolation considers the sixteen nearest grid cells of the original data to generate polynomial cubic splines in two directions.

Let’s try a basic interpolation downscaling. We will downscale the coarse hindcast to the higher-resolution observations. To use the Interpolation method with gridded data, we select `downscale_function = "Interpolation"`, select a regridding method (e.g. `method_remap = "bilinear"`), and provide a `target_grid` (a netCDF file containing the grid to which we want to downscale).

> 💡 Note: `target_grid` is often the same as the source files used to load the observed data.

    dwn <- c4h_downscale("Interpolation",
                         exp = hcst,
                         method_remap = "bilinear",
                         target_grid = paste0(rean_path, "t2m_201001.nc"))

You might see some warning messages related to the downscaling functionality - don’t worry, this is completely normal.

`c4h_downscale()` returns a list of `s2dv_cube` objects including the downscaled experimental (i.e. forecast or hindcast) and observational data. We can visualise the downscaled hindcast using `c4h_plot()`.

    c4h_plot(dwn$exp, ensemble = TRUE)

We can compare this to the observations. Now the hindcast spatial resolution has been increased.

    c4h_plot(rean)

> 💡 Note: The Interpolation method does not involve any bias adjustment, so we have simply increased the spatial resolution of data, without comparing any statistical relationships with the observed values. No new information (such as high-resolution observations) has been introduced, so the interpolation tends to smooth fields.

### Method 2: Interpolation plus bias correction

This method relies on an initial interpolation, as above.

Following this, a bias adjustment of the interpolated values is performed at each grid cell. Bias adjustment techniques include simple bias correction, calibration or quantile mapping.

- The simple bias correction technique assumes the data is well approximated by a Gaussian distribution, and adjusts the mean and standard deviation of the forecast data to match that of the reference.

- The calibration (EVMOS — Equal Variance Matching of Observations and Simulations) technique similarly adjusts the mean and variance of the forecast to match that of the reference dataset. It also addresses a common problem in ensemble forecasts known as underdispersion, where the spread of ensemble members does not fully capture the uncertainty in the forecast. EVMOS corrects for this by inflating the ensemble spread so that the forecast probabilities are better calibrated — meaning that, for example, a forecast probability of 70% should correspond to the event occurring approximately 70% of the time.

- The quantile mapping approach may take several forms. A commonly used approach, particularly for bias correcting precipitation forecasts, is the Empirical Quantile Mapping (EQM) method, based on the empirical cumulative distribution functions (CDFs) of the forecast and reference data sets. The transfer function from the forecast CDF to the reference CDF is obtained to bias-correct the forecast data; this method can capture the average evolution of, and variability in, precipitation while adjusting all statistical moments.

Let’s try using the Intbc method. Since we are downscaling temperature, let’s choose a bilinear interpolation and EVMOS. To use the Intbc method with gridded data, we select `downscale_function = "Intbc"`, select a regridding method (e.g. `method_remap = "bilinear"`), provide a `target_grid` (a netCDF file containing the grid to which we want to downscale), and select a bias correction method (e.g. `method_bc = "evmos"`).

    dwn <- c4h_downscale("Intbc", exp = hcst, obs = rean,
                         method_bc = "evmos", method_remap = "bilinear")

> 💡 Note: You will now see even more warnings related to the downscaling - again, this is completely normal. In this case, it is because we are using a reanalysis dataset which contains NA values over the ocean.

    c4h_plot(dwn$exp, ensemble = TRUE)

Note that now, by adjusting the data as well as simply interpolating it, we have managed to recapture some of the spatial variation in temperature seen in the observations.

### Method 3: Interpolation plus linear regression

This method relies on an initial interpolation, as above.

Following this, a linear-regression with the interpolated values is fitted using the higher-resolution observations as predictands, and then applied with model data to correct the interpolated values. Possible methods of regression are basic and a nearest neighbour (or stencil) method.

- The basic method fits a linear regression at each grid cell using high resolution observations as predictands and the interpolated model data as predictor. The regression equation is applied to the interpolated model data to correct the interpolated values.

- The nearest neighbour method uses a local linear regression with the nine nearest neighbours as predictors and high-resolution observations as predictands. Instead of constructing a regression model using all nine predictors, principal component analysis is applied to the data of neighboring grids to reduce the dimension of the predictors. The linear regression model is then built using the principal components that explain 95% of the variance. The nearest neighbour method does not require a pre-interpolation process.

We can now try the Intlr method. Let’s give a conservative regridding and basic linear interpolation a go. To use the Intlr method with gridded data, we select `downscale_function = "Intlr"`, select a regridding method (e.g. `method_remap = "conservative"`), provide a `target_grid` (a netCDF file containing the grid to which we want to downscale), and select a linear regression method (e.g. `method_lr = "basic"`). Suppose this time, we want to downscale the forecast rather than the hindcast - we can provide the forecast as `exp_cor` and the hindcast as `exp`.

    dwn <- c4h_downscale("Intlr", exp = hcst, obs = rean,
                         exp_cor = fcst,
                         method_lr = "basic",
                         method_remap = "con")

> 💡 Note: In both the Intbc and Intlr methods, it is not required to specify the argument `target_grid`. This is because `c4h_downscale()` will extract this from the metadata of the high resolution `obs`. This is not the case with the Interpolation technique, which may be used without specifying `obs`, and so the `target_grid` argument is required.

Again, we can visualise the downscaled data. Note that in this case, `dwn$exp` contains the downscaled forecast data (not the hindcast).

    c4h_plot(dwn$exp, ensemble = TRUE)

### Method 4: Analogs

A Perfect Prognosis (PP) method based on the popular analog technique, which infers the downscaled forecast from a set of analog situations selected from daily historical observational data. The search of the analogous fields is performed using the Euclidean distance, which estimates the similarity between large-scale forecast fields and their counterparts from historical reanalysis data. This approach is also known outside the climate community as an implementation of the k-nearest neighbours (K-NNs) algorithm (James 2021), considering each grid point as a feature and getting a multioutput.

The analogs method essentially matches observed large-scale atmospheric conditions (e.g., pressure patterns, temperature fields) with similar patterns simulated within the forecast. The high-resolution observed local climate associated with those patterns is then used as the downscaled climate data in the forecast. By default, only the first analog (i.e. the closest match) will be returned.

    dwn <- c4h_downscale("Analogs", exp = hcst, obs = rean)

Plot the output.

    c4h_plot(dwn$exp, ensemble = TRUE)

## 3. Downscaling to point locations

We can use the above methods to also downscale to point locations, rather than from a coarse grid to a fine grid.

To do this, let’s load some station data.

    stat_path <- system.file("extdata/stations/", package = "clim4health")
    point_locs <- clim4health::c4h_load(stat_path,
                                        ext = "csv",
                                        year = 2010:2012,
                                        month = 1,
                                        leadtime_month = 1:3,
                                        variable = "temp_mean")

    # use c4h_time to obtain monthly data
    point_locs <- c4h_time(point_locs, time_aggregation = "monthly", dim_aggregation = "sdate")

To downscale to point locations, we need to provide `points`, a named list of latitudes and longitudes. `c4h_load` has already saved these in the attribute `location`. We also need to provide the `method_point_interp` argument to `c4h_downscale()`.

    points <- list(latitude  = point_locs$attrs$location$latitude,
                   longitude = point_locs$attrs$location$longitude)

    dwn <- c4h_downscale("Interpolation", exp = hcst,
                         points = points, method_point_interp = "bilinear")

> 💡 Note: In the case of point downscaling, if using `Intbc` or `Intlr` both `exp` and `obs` will be downscaled to the location of the points, and only regular gridded data is allowed as input for `exp`/`obs`.

Let’s plot the output of this downscaling.

    c4h_plot(dwn$exp, ensemble = TRUE, boundaries = "countries")

We could also apply an `Intbc` or `Intlr` downscaling to point locations. For example:

    dwn <- c4h_downscale("Intbc", exp = hcst, obs = rean,
                         points = points, method_point_interp = "bilinear",
                         method_bc = "evmos")

## 4. Calibration

We can also calibrate climate data (this is similar to downscaling, but we will use calibration to refer to the bias adjustment of polygon, or areal, data). In this case there is then no interpolation step as we do not need to regrid the data. Instead, data are compared for each spatial region instead of by grid cell.

First, let’s aggregate the gridded data to polygons.

    library(sf)

    # Region municipalities
    munip_path <- system.file("extdata", "areas", "munip_vallecauca.gpkg",
                            package = "clim4health")
    munip <- read_sf(munip_path)

    hcst_aggr <- c4h_space(hcst, munip)
    rean_aggr <- c4h_space(rean, munip)

Now we can use `c4h_downscale()` to calibrate the polygon data.

    cal <- c4h_downscale("Intbc", exp = hcst_aggr, obs = rean_aggr,
                         method_bc = "bias")

We can plot the raw hindcast data, the calibrated hindcast data, and the observations. To plot the data using `boundaries = "countries"`, you must have the suggested package `spData` installed.

    c4h_plot(hcst_aggr, ensemble = TRUE, boundaries = "countries")
    c4h_plot(cal$exp,   ensemble = TRUE, boundaries = "countries")
    c4h_plot(rean_aggr, ensemble = TRUE, boundaries = "countries")

> 💡 Note: In this case, because we have only used 3 years of data, there was not enough information to calibrate the data and only NA values were returned for the calibrated output.

## 5. Considerations for downscaling common variables

The choice of parameters for your downscaling is important, and can vary between different variables!

#### Interpolation-based methods

- Bilinear interpolation smoothes the data field, resulting in reduced maxima and increased minima - if you are interested in extremes this may not be the most appropriate method.

- Bicubic interpolation may result in values outside the range of the original data; for some variables (e.g. temperature) this is acceptable, but for others (e.g. precipitation, which cannot take values below zero) this is not.

#### Specific recommendations for precipitation downscaling

- If you are interested in downscaling precipitation, it is important to choose a regridding method that preserves the total amount of precipitation. We therefore recommend using the conservative remapping within the `Interpolation`, `Intbc`, and `Intlr` downscaling methods.

- Similarly, precipitation cannot be assumed to follow an approximately Gaussian (normal) distribution (as many values will be 0, and no values below this). Therefore we do not recommend the simple bias correction method.

- `quantile_mapping` bias correction may be most appropriate in the case of precipitation. For precipitation downscaling, you could also apply the argument `wet.day = TRUE`, which attempts to equalise the fraction of days with precipitation between `obs` and `exp` - in this case, the empirical probability of nonzero observations is found (`obs$data>0`) and the corresponding value in `exp` becomes a threshold below which all values are set to zero.

#### General recommendations

⚠️ When using the Analogs method, use daily data (not monthly) to search for the closest matches.

You need at least 20 years of data to perform a robust statistical downscaling. The longer the timeseries available, the better. This can result in a heavier computational cost, but more robust relations between `obs` and `exp`.

## Parameter selection

`c4h_downscale()` has many optional parameters. The diagram below can be used as a guide to select the appropriate parameters, depending on the `downscale_function` chosen and the type of data being downscaled (gridded, point, polygon). Not all arguments are shown!

In particular, we note one final optional parameter, `loocv` (leave-one-out cross-validation). The default of this parameter is `TRUE`, which is generally recommended when downscaling hindcast data (i.e. when `exp_cor` is `NULL`). In the case of `loocv = TRUE`, when applying the bias correction or building the regression model for a given year, the corresponding values from that year are removed. When downscaling forecast data (i.e. `exp_cor` is not `NULL`), this may be set to `FALSE`.