Model Overall Exposure Scores Using Time Series Data

This function statistically evaluates the exposure to a pressure, based on time series data. The scoring is based on the paper of Gaichas et al., 2014: A risk-based approach to evaluating northeast US fish community vulnerability to climate change. The exposure scoring is split into four components: magnitude (or degree of change), frequency of change, the future trend of the pressure, and spatial scale. Uncertainty of the exposure assessment is evaluated using general additive models (GAM) and an autoregressive integrated moving average model (ARIMA).

Usage

model_exposure(
  pressure_time_series,
  base_years = NULL,
  base_years_by_press = NULL,
  current_years = NULL,
  current_years_by_press = NULL,
  trend = "return",
  spatial = 3
)

Arguments

pressure_time_series

A data frame (not a tibble object) with time series of pressures to be evaluated. First column MUST be the time column.

base_years

A vector with two numerics, specifying the time period for the baseline. The first one start is the starting year for all pressures and the second one end is the end of the baseline for all pressures. The default is NULL. One can specify pressure specific baseline periods using the base_years_by_press argument. If base_years and base_years_by_ind are NULL, then the first 5 years of the time series are used as baseline period.

base_years_by_press

A data frame, specifying the baseline years for each pressure individually, by setting the starting year (second column) and the end year (third column). The first column must contain the names of the pressure indicators used in pressure_time_series. The default is NULL. If base_years and base_years_by_press are NULL, then the first 5 years of the time series are used as baseline period.

current_years

A vector with two numerics, specifying the time period for the assessment period. The first one start is the starting year for all pressures and the second one end is the end of the assessment period for all pressures. The default is NULL. One can specify pressure specific assessment periods using the current_years_by_press argument. If current_years and current_years_by_press are NULL, then the last 5 years of the time series are used as assessment period.

current_years_by_press

A data frame, specifying the assessment period for each pressure individually, by setting the starting year (second column) and the end year (third column). The first column must contain the names of the pressure indicators used in pressure_time_series. The default is NULL. If current_years and current_years_by_press are NULL, then the last 5 years of the time series are used as assessment period.

trend

a character vector specifying whether a trend returning to the baseline conditions should be considered as good or a trend further leaving the baseline conditions. Possible inputs are return or leave.Default is not specified is return, meaning a return to the baseline is desired.

spatial

a vector with scores for the spatial scale of each pressure. The default is 3 for each pressure, meaning that 40 - 60% of the entire assessment area is affected. Scores should be on a scale from 1 - 5, depending on the percent of area that is affected by the pressure:

1: < 20%,
2: 20 - 40%,
3: 40 - 60%,
4: 60 - 80%,
5: > 80%.

Value

a data frame containing the pressure names, the aggregated exposure score and scores for magnitude, frequency, future trend and spatial scale of the pressures, the final uncertainty score and uncertainty scores of the ARIMA and the GAM. If default settings are used, the following data frame will be returned:

pressure: Name of the assessed pressure.
exposure: Exposure score, mean of the four assessed exposure components.
uncertainty: Uncertainty score associated with the exposure assessment.
comp_magnitude: Score for the magnitude of change.
comp_frequency: Score for the frequency of a significant deviation from baseline conditions.
comp_trend: Score for the future trend of the pressure.
comp_direction: Direction of the development of the pressure in the assessment period.
comp_spatial: Score for the spatial scale, either set by the user or automatically set to 3.
uncertainty_arima: Uncertainty score based on the ARIMA model.
uncertainty_gam: Uncertainty based on the GAM.
mean_baseline: Mean of the baseline conditions, used for magnitude scoring.
mean_current: Mean of the current conditions, used for magnitude and frequency scoring.
standard_deviation_baseline: Standard deviations of the baseline conditions. Used for scoring of magnitude and frequency.
slope_linear_model: Slope of the linear model used for scoring the future trend and to determine the direction.
p_value_linear_model: P-value of the linear model, used to score the future trend.

Details

All components are scored on a scale from 1 - 5, low impact to high impact. The degree of change compares the mean of the current time period to the baseline time period, the score is based on standard deviations. The frequency evaluates in how much percent of the current time period the mean deviates more than one standard deviation from the baseline mean. The future trend scores if the pressure will in the future be in desired conditions or not. Usually this means the pressure returns to the baseline conditions. The overall exposure score is the mean of all four components. Uncertainty of exposure is evaluated using a general additive model and an autoregressive integrated moving average model (ARIMA). The models are fitted using the time series except the assessment period. The assessment period is then predicted. The function evaluates how many of the observed data points are within the predicted 95% confidence interval. If more than 66 % are within the 95% CI the uncertainty is 1 (low), if less than 33 % are within it, the uncertainty is set to 3 (high). Additionally the function compares the mean size of the predicted 95% confidence interval and compares it to the maximum range of the observed data points to account for very large confidence intervals, which would otherwise lead to too optimistic uncertainty scores. The lower uncertainty score is selected as final uncertainty score. The time periods of baseline and assessment period have to be carefully set to reflect ongoing dynamics. Especially for oscillating pressures time periods should be longer to assess the overall trend and not the oscillation itself.

Examples

### Example with 3 pressure time series in the demo data 'pressure_ts_baltic'
#   where the first 11 years represent the general baseline period and the last
#   7 years of the time series the current assessment period:
sub_ts <- pressure_ts_baltic[ ,c("year", "surf_temp_sum", 
  "surf_sal_sum", "bot_oxy_ann")]
model_exposure(
  pressure_time_series = sub_ts ,
  base_years = c(start = 1984, end = 1994),
  current_years = c(start = 2010, end = 2016)
)
#>        pressure exposure uncertainty comp_magnitude comp_frequency comp_trend
#> 1 surf_temp_sum     3.00           2              2              4          3
#> 2  surf_sal_sum     3.25           2              2              5          3
#> 3   bot_oxy_ann     3.50           2              2              5          4
#>   comp_direction comp_spatial uncertainty_arima uncertainty_gam mean_baseline
#> 1       increase            3                 2               2     13.360030
#> 2       decrease            3                 2               3      5.935398
#> 3       decrease            3                 2               2      4.466583
#>   mean_current standard_deviation_baseline slope_linear_model
#> 1    14.895450                    1.344546         0.06988084
#> 2     5.574401                    0.193843        -0.02150520
#> 3     4.001809                    0.253705        -0.36222659
#>   p_value_linear_model
#> 1           0.74663270
#> 2           0.92121801
#> 3           0.03754337

### Example with 2 pressure time series and pressure-specific periods
sub_ts <- pressure_ts_baltic[ ,c("year", "nitrogen", "phosphorous")]
model_exposure(
  pressure_time_series = sub_ts,
  base_years_by_press = data.frame(
    press = c("nitrogen", "phosphorous"),
    start = c(1984, 1990), end = c(1994, 2000)),
  current_years_by_press = data.frame(
      press = c("nitrogen", "phosphorous"),
      start = c(2010, 2012), end = c(2016, 2016))
)
#>      pressure exposure uncertainty comp_magnitude comp_frequency comp_trend
#> 1    nitrogen     3.50           2              3              5          3
#> 2 phosphorous     2.25           2              1              2          3
#>   comp_direction comp_spatial uncertainty_arima uncertainty_gam mean_baseline
#> 1       increase            3                 2               2    19.9366961
#> 2       decrease            3                 2               2     0.5810386
#>   mean_current standard_deviation_baseline slope_linear_model
#> 1   22.6823144                  1.27570100        0.002903849
#> 2    0.6408257                  0.07574186       -0.017404547
#>   p_value_linear_model
#> 1            0.9893508
#> 2            0.9649661