Interpolation of daily mean air temperature data via spatial and non-spatial copulas

Transcription

1 Interpolation of daily mean air temperature data via spatial and non-spatial copulas F. Alidoost, A. Stein 6 July 2017

2 Research problem 2 Assessing near-real time crop and irrigation water requirement using crop growth simulations. Daily mean air temperature is an input for crop growth simulations. Weather stations are sparse and located at irregular positions. The results of crop growth simulations at unvisited locations are likely to be uncertain. Weather station

3 Research problem 3 To use weather data from weather forecasting systems. Advantage: Gridded data Temporal resolution (daily) Limitations: Coarse spatial resolution Bias Weather station Weather forecasting system s points

4 Objective 4 Producing daily air temperature map at 1km spatial resolution via copulas interpolation: based upon non-spatial copulas including covariates to capture the spatial variability. providing a procedure for interpolation when a relatively low number of observations is available. including more than one covariate, allows one to analyze the effects of combining several covariates.

5 Copula /kɒpjʊlə/ The namecomes from the Latin for "link" or "tie". " 5 Joint distribution function to join multivariate distribution function to marginal distribution functions. Independent variables: Correlated variables: or Empirical marginal distribution function, F : =

6 Copula 6 copula density: strength of dependence Sklar s theorem: = copula conditional copula density: conditional copula: =

7 Copula-based interpolation methods 7 Expectation predictor: An unvisited location For an unvisited location & its n nearest neighbors

8 Copula-based interpolation methods Predictor #1: At an unvisited location, : = 8 For an unvisited location & its n nearest neighbors:

9 Copula-based interpolation methods Predictor #2: At an unvisited location, : = 9 For an unvisited location & its n nearest neighbors: m covariates for an unvisited location

10 Copula-based interpolation methods Predictor #3: At an unvisited location, : = 10 For an unvisited location & its n nearest neighbors & its m covariates: Non-spatial copula at an nearest neighbor and its m covariates: m covariates for an unvisited location =

11 Study area Irrigation network, Qazvin plain, Iran N 35.99,49.64 E Weather station 50.59

12 Dataset Daily mean air temperatures on 6 June 2004 to 2014: 24 weather stations 150 ECMWF* bias corrected points at approximately 13.5 km spatial resolution 12 *ECMWF: European Centre for Medium-Range Weather Forecasts Weather station ECMWF points

13 Dataset Three covariates at 1km spatial resolution for air temperature on 6 June Sources: Landsat 8 and SRTM Leaf area index (LAI, m2/m2) 326 Height (m) Land surface temperature (LST, ºK)

14 Implementation 14 Marginal distribution function: fitting a spline to eleven years series of weather station data. Retrieving covariates at different spatial resolutions: applying a mean filter to retrieve covariates at 1km spatial resolution. Spatial copulas: selecting five copula families such as Gaussian, Student s t, Clayton, Gumbel and Frank for correlogram. Non-spatial copulas: classifying the study area to vegetation and non-vegetation area based on NDVI. Number of nearest neighbours: 8 Implementation in R: using the packages gstat, copula, spcopula and VineCopula.

15 Validation For three predictors: Cross-validation Statistics comparison Spatial variability 15 Predictor #1 (Gräler 2014): Predictor #2 (New!, type and number of covariates): Predictor #3 (New!, spatial and non-spatial copulas):

16 Results: Statistics comparison 16 Cross-validation Predictor #1 Predictor #2 Predictor #3 Mean absolute error Observations Statistics Weather stations Predictor #1 Predictor #2 Predictor #3 Average Standard deviation Coefficient of variation Minimum Maximum

17 Results: Statistics comparison Bias correction Mean air temperature (ºC) Predictor #1 Weather stations + ECMWF Predictor #2 LST Height LAI Predictor #3

18 Results: Spatial variability Weather stations + ECMWF(bias-corrected) 25.2 Obtained by predictor # Obtained by predictor #2 Obtained by predictor #3 14.7

19 Discussion Main sources of uncertainty: Correcting for bias in the weather forecasting system data Retrieving covariates using remote sensing images Spatial variability of daily mean air temperature at 1km spatial resolution Parameters in the implementation: Marginal distribution function Copulas families Number and type of the covariates Correlogram (spatial copulas) Number of the nearest neighbors Next steps: Comparing with other interpolators Sensitivity analysis for the covariates Considering prediction interval width 19

20 Conclusion 20 The new methods are beneficial for the local refinement of weather data if a low number of observations is available and one is interested in predicting the spatial variability of the weather parameter. We contributed to VineCopula package to interpolate the random field spatially using more than one covariate.

21 21 Thank You Due to averaging, almost all interpolation methods will underestimate the highs and overestimate the lows. And if an interpolation methods didn t average, we wouldn t consider it reasonable! (Geoffrey Bohling, 2005)