This paper presents spatial interpolation techniques to produce finer-scale daily rainfall data from regional climate modeling. Four common interpolation techniques (ANUDEM, Spline, IDW, and Kriging) were compared and assessed against station rainfall data and modeled rainfall. The performance was assessed by the mean absolute error (MAE), mean relative error (MRE), root mean squared error (RMSE), and the spatial and temporal distributions. The results indicate that Inverse Distance Weighting (IDW) method is slightly better than the other three methods and it is also easy to implement in a geographic information system (GIS). The IDW method was then used to produce forty-year (1990–2009 and 2040–2059) time series rainfall data at daily, monthly, and annual time scales at a ground resolution of 100 m for the Greater Sydney Region (GSR). The downscaled daily rainfall data have been further utilized to predict rainfall erosivity and soil erosion risk and their future changes in GSR to support assessments and planning of climate change impact and adaptation in local scale.
Rainfall is a highly important piece of data which is frequently required for water resource management, hydrologic and ecologic modeling, recharge assessment, and irrigation scheduling. Such data are normally recorded as observational data through comprehensively designed rainfall station networks. However, rainfall records are often incomplete because of missing rainfall data in the measured period or insufficient stations in the study region.
More recently, global climate models (GCMs) are widely used for assessing the responses of the climate system to changes in atmospheric forcing. Projections of potential climate change are essential for sustainable natural resources planning and management [
Climate projections at 2 km resolution provide increased level of detailed information for fire and emergency management, water and energy management, agriculture, urban planning, and biodiversity management which need to adapt to a future climate [
There are many varieties of spatial interpolation techniques and they can be classified into three categories based on interpolation methods and scales of application. The first category includes Nearest Neighbor (NN), Thiessen polygons, Spline, and various forms of Kriging and Inverse Distance Weighting (IDW) which are frequently used in interpolating rainfall data from rain gauge stations [
Many studies have been dedicated to the comparison and evaluation of different spatial interpolation methods at various spatial scales. For example, Dirks et al. [
This study differs in several ways from previous ones. It specifically aimed to compare spatial interpolation methods for rainfall time series predicted from regional climate models (through the NARCliM project) for the current climate period and determine the suitable method to produce daily rainfall GIS layers for the future climate periods. The interpolated daily rainfall data have been directly used in rainfall erosivity and soil erosion risk modeling [
We chose Greater Sydney Region (GSR) as the study area because
The boundary of the GSR is defined as 148.8°E to 152.4°E and 35.7°S to 32.4°S and covers an area of 124,000 km2 (Figure
Locational map of the Greater Sydney Region (GSR), rainfall station sites, and state plan regions within GSR.
This dataset has been developed by the Australian Water Availability Project (AWAP) and details on the creation of AWAP can be found in Jones et al. [
The New South Wales Office of Environment and Heritage (OEH) and the Climate Change Research Centre at the University of New South Wales (UNSW) are developing an ensemble of future climate projections using regional climate models. The NARCliM project provides projected climate data for adaptation to a future climate for NSW and the Australian Capital Territory. The Sydney climate projections used in this study have been developed by UNSW as a pilot study using the GCM (CSIRO MK 3.5) and regional climate models. This model is just one of a suite of GCMs available for the GSR and was chosen because it performed best in replicating observed climate despite uncertainties in the downscaling sourced from the GCMs [
Four different interpolation methods (IDW, Kriging, ANUDEM, and Spline) were tested in this study to interpolate the 2 km data from the NARCliM project to a finer resolution of 100 m. We chose these methods as they are representative of available interpolation procedures, widely used in rainfall interpolation, and easy to implement in GIS (e.g., ESRI’s ArcGIS).
IDW interpolation determines cell values using a weighted combination of a set of sample points. The weight is a function of the inverse distance [
Kriging is perhaps the most distinctive interpolation method [
ANUDEM was developed at the Australian National University [
Spline performs a two-dimensional minimum curvature spline interpolation on a point dataset resulting in a smooth surface that passes exactly through the input points [
The above spatial interpolation techniques were implemented in ESRI’s ArcGIS with the following procedures:
Automated GIS scripts have been developed for all the above procedures to process the projected daily rainfall data (originally in ASCII format) and spatially interpolate them into 100 m grids. A rainfall filter is applied such that any daily rainfall event above a maximum threshold (350 mm/day [
In this study, mean absolute error (MAE), mean relative error (MRE), and root mean squared error (RMSE) were used to assess the performances of the four interpolation methods. MRE reflects the relative accuracy of the interpolation, and the MAE and RMSE are indicators of the magnitude of extreme errors. Lower MAE, MRE, and RMSE values indicate greater central tendencies and generally smaller extreme errors. In the meantime, the coefficient of correlation
With the aid of the automated GIS scripts developed in this study, we interpolated daily rainfall for the recent (1990–2009) and future (2040–2059) periods using the four interpolation methods as described above. We produced 13,318,880 daily, 1,920 monthly, and 140 annual rainfall GIS layers covering a 40-year period.
The monthly and annual rainfall values (calculated from the interpolated daily rainfall) from the four interpolation methods were used in the assessment and evaluation as the comparison at daily step would be otherwise too complicated. We sampled the monthly and annual rainfall data at the 72 rainfall station sites [
We compared MAE, MRE, RMSE, and
Interpolation errors of monthly rainfall.
Interpolation methods | MAE | MRE | RMSE |
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IDW | 42.81 | 0.55 | 66.81 | 0.55 |
Kriging | 43.05 | 0.55 | 67.21 | 0.54 |
ANUDEM | 43.27 | 0.56 | 67.57 | 0.54 |
Spline | 43.30 | 0.56 | 67.58 | 0.54 |
Interpolation errors of annual rainfall.
Interpolation methods | MAE | MRE | RMSE |
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IDW | 243.11 | 0.26 | 313.02 | 0.54 |
Kriging | 245.08 | 0.26 | 316.60 | 0.54 |
ANUDEM | 246.98 | 0.26 | 319.59 | 0.53 |
Spline | 246.99 | 0.27 | 322.78 | 0.53 |
Scatter plots of correlation between interpolation and AWAP for monthly rainfall (a) and annual rainfall (b).
The error analysis also shows regional variation revealing that the interpolation accuracy is generally higher in the Western regions (Western and South Western) than the coastal regions (Tables
Error assessment of interpolated monthly rainfall in state plan regions.
Interpolation methods | SPR | MAE | MRE | RMSE |
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IDW | Northern Beaches | 51.29 | 0.55 | 78.94 | 0.50 |
Eastern/Inner | 55.06 | 0.78 | 77.60 | 0.48 | |
Western | 49.75 | 0.73 | 73.14 | 0.46 | |
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Kriging | Northern Beaches | 50.34 | 0.54 | 78.32 | 0.49 |
Eastern/Inner | 55.95 | 0.73 | 83.17 | 0.42 | |
Western | 37.95 | 0.55 | 58.08 | 0.56 | |
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ANUDEM | Northern Beaches | 51.78 | 0.56 | 79.46 | 0.49 |
Eastern/Inner | 48.96 | 0.58 | 74.94 | 0.48 | |
Western | 38.02 | 0.55 | 58.20 | 0.56 | |
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Spline | Northern Beaches | 52.03 | 0.56 | 79.76 | 0.49 |
Eastern/Inner | 45.72 | 0.56 | 69.41 | 0.52 | |
Western | 48.61 | 0.57 | 36.31 | 0.56 |
Error assessment of interpolated annual rainfall in state plan regions.
Interpolation methods | SPR | MAE | MRE | RMSE |
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IDW | Northern Beaches | 278.23 | 0.25 | 346.52 | 0.42 |
Eastern/Inner | 244.45 | 0.25 | 307.68 | 0.45 | |
Western | 253.96 | 0.25 | 323.46 | 0.32 | |
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Kriging | Northern Beaches | 328.30 | 0.40 | 422.52 | 0.32 |
Eastern/Inner | 332.90 | 0.30 | 410.30 | 0.42 | |
Western | 223.73 | 0.27 | 287.36 | 0.48 | |
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ANUDEM | Northern Beaches | 280.85 | 0.25 | 350.27 | 0.42 |
Eastern/Inner | 246.63 | 0.26 | 310.56 | 0.45 | |
Western | 224.22 | 0.27 | 288.09 | 0.45 | |
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Spline | Northern Beaches | 283.10 | 0.25 | 353.04 | 0.41 |
Eastern/Inner | 248.35 | 0.26 | 312.74 | 0.45 | |
Western | 222.26 | 0.27 | 285.14 | 0.48 |
The spatial variations of monthly rainfall interpolated by all four methods have similar patterns (Figure
Comparison of interpolation methods for mean monthly rainfall against AWAP.
The spatial patterns of annual rainfall patterns of the four interpolation methods are similar to those with predicted mean annual rainfall value around 883 mm (882.7–883.2 mm). The minimum values of annual rainfall from IDW, Kriging, ANUDEM, and Spline interpolation methods are 599.7 mm, 599.1 mm, 595.7 mm, and 567.2 mm, and the maximum values are 1481.9 mm, 1483.2 mm, 1485.2 mm, and 1491.1 mm, respectively. Again, higher values of annual rainfall appeared in the far-Western district and the coastal districts, and lower values mainly appear in Southern, Northern Beaches, and Eastern-Inner districts. The IDW and Kriging, as they emphasize the significant of known points upon the interpolated values, produced more localized patterns. But the Spline and ANUDEM generated more smooth surfaces (Figure
Comparison of interpolation methods for annual mean rainfall against AWAP.
The monthly and annual rainfall patterns in the GSR are similar and consistent from the four interpolation methods. That is, the mean values in the Northern region are always higher than those of the Western and Southern regions for all the interpolation methods. The interpolated monthly and annual rainfall patterns show the obvious rainfall increase from west to east, but such trend in the north-south direction is not obvious.
Compared with the AWAP rainfall, the interpolated rainfall shows similar seasonal variations within the GSR (Figure
Comparisons of seasonal mean rainfall from AWAP and the four interpolation methods in Greater Sydney Region.
In general, there is more rainfall from January to May, and little from July to September. The maximum, minimum, and annual values of future rainfall are increasing compared with the recent period and this might be due to the GCM (CSIRO MK 3.5) itself which is regarded as a “wetter” model (overestimate rainfall [
Monthly rainfall and variation between interpolation and AWAP.
Future rainfall is predicted to increase significantly by 2050 in GSR using this specific climate model (CSIRO MK 3.5, Figure
Predicted temporal change of rainfall in Greater Sydney Region.
To assess the impacts of projected rainfall on soil erosion risk, we further applied an improved daily rainfall erosivity model [
Mean rainfall (mm⋅yr−1), rainfall erosivity (MJ⋅mm⋅ha−1⋅hr−1⋅yr−1), hillslope erosion (tonnes⋅ha−1⋅yr−1), and their changes over the two contrasting periods (1990–2009 and 2040–2059). Change% is calculated as (Future − Recent)/Recent.
SPR name | Eastern/Inner | Northern | Northern Beaches | Southern | South Western | Western | All SPRs |
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Recent annual rainfall | 1094.46 | 1120.51 | 1243.44 | 1142.75 | 851.60 | 948.59 | 946.18 |
Future annual rainfall | 1516.21 | 1410.26 | 1643.75 | 1550.36 | 1043.67 | 1215.87 | 1202.27 |
Annual rainfall change (%) |
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Recent rainfall erosivity | 3381.53 | 3480.30 | 3985.32 | 3534.32 | 2162.49 | 2722.00 | 2654.13 |
Future rainfall erosivity | 6027.67 | 5481.52 | 6604.56 | 6222.66 | 3622.83 | 4261.81 | 4295.57 |
Rainfall erosivity change (%) |
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Recent hillslope erosion | 0.99 | 8.48 | 8.54 | 4.97 | 3.22 | 8.41 | 6.79 |
Future hillslope erosion | 2.05 | 13.57 | 14.57 | 9.82 | 6.00 | 13.56 | 11.04 |
Hillslope erosion change (%) |
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Modeled mean annual rainfall erosivity and hillslope erosion in Sydney Region.
In this study, four common but representative spatial interpolation methods have been applied to downscale RCM modeled rainfall data into high-resolution GIS data layers. The results of our study show that the projected rainfall data, at monthly and annual scales, are close to the AWAP data in spatial patterns despite about 7% deference in absolute values as the GCM (CSIRO MK 3.5) generally overestimates rainfall particularly in autumn, and the
In our study, IDW, ANUDEM, and Spline interpolation methods produced very similar results and they all reveal similar patterns of monthly rainfall distributions, while Kriging produced slightly different seasonal patterns. The study suggests that IDW is slightly superior, though not significantly, to others in relative errors and computational efficiency.
The four interpolation methods also resulted in similar spatial patterns across GSR and they all show the obvious variations across the state plan regions. Predicted rainfall tends to gradually reduce from East to West and from Eastern/Inner to Northern Beaches. All four interpolation methods produced more reasonable estimations in Western district than Northern or Eastern/ Inner district as the rainfall patterns in the latter district are more variable. This implied that the ordinary interpolation methods can not accurately reflect extremes in monthly and annual rainfall patterns. While they are similar, we chose IDW interpolation method as it performed slightly better, and it is easier and faster in computation and compatible with previous ones [
There is likely significant increase in rainfall erosivity and soil erosion risk based on the rainfall projections used in this study. The predicted future soil erosion risk and the changes are useful information for climate impact assessments and adaptation and planning. In the near future, we will extend the techniques developed in this study to produce daily rainfall data at a resolution adequate for local soil erosion risk prediction from climate projections for the entire south-east Australia. The NARCliM projected daily rainfall data (at 10 km spatial resolution) from all 12 ensembles (4 GCMs and 3 RCMs [
In conclusion, this study has demonstrated a suitable approach and processes to interpolate daily rainfall values for recent and future periods from GCM projections. The methods have been successfully implemented in GIS for efficient calculation and mapping of the spatial and temporal variation of rainfall across GSR. The spatial interpolation greatly enhanced the level of detail which is useful for climate impact assessments and soil erosion modeling at local scale. With the automated GIS process developed in this study, the daily rainfall GIS layers, consequently rainfall erosivity and soil erosion layers, can be readily upgraded when better or future rainfall data become available. The methodology and GIS programs are also readily applicable to any other regions with GCM projections at about the same resolution.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This project was supported by the NARCliM program managed by New South Wales Office of Environment and Heritage (OEH). The authors thank the NARCliM project team at University of New South Wales and Climate Science team at OEH for providing the projected daily rainfall data. They also thank Jiangsu State Government for providing scholarship for Dr. Xiaojin Xie for her six-month visit to OEH where she worked on this project.