Research Article: The use of bivariate copulas for bias correction of reanalysis air temperature data

Date Published: May 8, 2019

Publisher: Public Library of Science

Author(s): Fakhereh Alidoost, Alfred Stein, Zhongbo Su, Yajie Zou.


Air temperature data retrieved from global atmospheric models may show a systematic bias with respect to measurements from weather stations. This is a common concern in local climate studies. The current study presents two methods based upon copulas and Conditional Probability (CP) to predict bias-corrected mean air temperature in a data-scarce environment: CP-I offers a single conditional probability as a predictor, CP-II is a pixel-wise version of CP-I and offers spatially varying predictors. The methods were applied on daily air temperature in the Qazvin Plain, Iran that were collected at 24 weather stations and 150 ECMWF ERA-interim grid cells from a single month (June) over 11 years. We compared the methods with the commonly applied conditional expectation and conditional median methods. Leave-k-out cross-validation and correlation scores show that the new methods reduced the bias with 44–68% for the full data set and with 34–74% on a homogeneous subarea. We conclude that the two methods are able to locally improve ECMWF air temperatures in a data-scarce area.

Partial Text

Assessment of the impact of climate change in agricultural areas is primarily based upon changes in weather data such as air temperature [1]. In a data-scarce environment, i.e., where weather stations are sparse, additional data are required. The European Centre for Medium-range Weather Forecasts (ECMWF) provides gridded ERA-interim reanalysis weather data that are being used increasingly [2]. They are prone to uncertainty because of the coarse resolution of models and variability of model parameters in space and time [3,4]. When compared with the measurements from weather stations, their bias is often considerable [5], in particular, if those measurements serve as benchmarks from which any measurement errors are ignored.

The structural, one sided difference between a measured value from a weather station x, and an ECMWF reanalysis value y is defined as the bias in ECMWF reanalysis values. We assume that the data are observed from two spatio-temporal random variables X and Y. In our study, the basis of the copula-based bias correction is a distribution function that allows for modeling the dependence structure between X and Y. The purpose of bias correction is to obtain x^0 that denotes a predicted value at an unvisited location. An unvisited location is an ECMWF grid point without a measurement.

The bias correction methods are compared in an actual study on air temperature data in the Qazvin irrigation network, Iran (Fig 1). The study area extends from 35.44° to 36.68° latitudes (N) and from 49.09° to 50.92° longitudes (E) and it includes 24 weather stations (Fig 1). The Qazvin area is one of the oldest agricultural areas in the world where maize, wheat, barley and orchards are the dominating crops. Besides it contains urban areas and natural vegetation. The European Centre for Medium-Range Weather Forecasts (ECMWF) provides reanalysis data at a wide range of spatial resolutions, e.g. regular and rotated lat/lon grids, and reduced Gaussian grid. For the dissemination, air temperature is bi-linearly interpolated to a 0.125° lat/lon grid at three hourly intervals. A grid of 10 × 15 cells covers the study area (Fig 1). ERA-Interim provides widely used global atmospheric reanalysis data [3]. The reanalysis air temperatures are retrieved for 150 grid cells at a 0.125° lat/lon resolution from the ERA-Interim data assimilation system.

In this paper, we presented and evaluated two new bias correction methods for air temperature that take temporal and spatial variations into account. The CE and CM methods produce smooth maps, assuming spatial stationarity when estimating the dependence structures between the measured and the reanalysis weather data. We proposed to use different conditional probabilities minimizing the bias in space to improve spatial variation of the bias-corrected values. In addition, we described the dependence structure between the measured and the reanalysis weather data using the flexibility of selecting best fitting family among five copula families.

We proposed to use conditional probabilities to correct for bias in the gridded reanalysis weather data provided by ECMWF as compared to the measurements from weather stations taken as the benchmarks. Cross-validation results and correlation scores showed that the new methods perform better than commonly applied methods and are able to account for spatial and temporal variation of air temperatures at unvisited locations.




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