Comparison of three interpolation methods for the average monthly temperature in the south of Iraqi zone

This study focuses on evaluating the suitability of three interpolation methods in terms of their accuracy at climate data for some provinces of south of Iraq. Two data sets of maximum and minimum temperature in February 2008 from nine meteorological stations located in the south of Iraq using three interpolation methods. ArcGIS is used to produce the spatially distributed temperature data by using IDW, ordinary kriging, and spline. Four statistical methods are applied to analyze the results obtained from three interpolation methods. These methods are RMSE, RMSE as a percentage of the mean, Model efficiency (E) and Bias, which showed that the ordinary krigingis the best for this data from other methods by the results that have been obtained .

Statistical evaluation is to understand statistical properties associated with the data set.These properties may include distribution, location, spread, and shape of the data set.There are many tools available in the univariate description statistics which can be used to describe these properties.For example, the frequency table and corresponding histogram can be used to describe how often observed values fall within certain intervals or classes.Probability plot can be used to determine how close the distribution of the data set is to a Gaussian or normal distribution [5].

Study area and Data used
The study area is located in the south of Iraq which includes a number of climatology of stations located in some of the southern provinces.The data used in this study, are Administrative map of Iraq as paper, with scale (1:100,000) and software used such as ERDAS, ArcGIS.

1-Inverse Distance Weights (IDW)
This a deterministic interpolation technique that creates surface from measured points, based on either the extent of similarity.The inverse distance weight technique provides an interpolation using s linearly combination of the temperature locations.To predict a value for any unmeasured location, IDW will use the measured values surrounding the prediction location.Those measured values closest to the prediction location will have more influence on the predicted value than those farther away.Thus, IDW assumes that each measured point has a local influence that diminishes with distance [7].

2-Spline
The Spline method can be thought of as fitting a rubber-sheeted surface through the known points using a mathematical function.In ArcGIS, the spline interpolation is a Radial Basis Function (RBF).These functions allow analysts to decide between smooth curves or tight straight edges between measured points.Advantages of splining functions are that they can generate sufficiently accurate surfaces from only a few sampled points and they retain small features.A disadvantage is that they may have different minimum and maximum values than the data set and the functions are sensitive to outliers due to the inclusion of the original data values at the sample points.This is true for all exact interpolations, which are commonly used in GIS, but can present more serious problems for Spline since it operates best for gently varying surfaces,(i.e.those having a low variance), [8].

3-Ordinary kriging
Ordinary kriging is the basic form of kriging .The prediction by ordinary kriging is a linear combination of the measured values.The spatial correlation between the data, as described by variogram, determines the weights.As the mean is unknown, fewer assumptions are made.The method assumes intrinsic stationarity, unfortunately meteorological variables are often not stationary.In some case this problem can be eliminated by using different sizes and shapes of the search nieghbourhood.Ordinary kriging is frequently applied in meteorology, often as part of residual kriging or indicator kriging [9].

Qualitative Measures of Estimation Accuracy
In this study, four statistical are used to characterize the performance of interpolation methods.They are, RMSE, RMSE as a percentage of mean observed temperature, bias and model efficiency.These statistics are described in equations ( 1), ( 2),(3),and (4).Standard error of interpolation surfaces are often expressed as percentage of the mean, due to the nature of the distribution of temperature (Hutchinson 2004).The RMSE of estimated temperature is based on the number of data and it is useful to quote the RMSE as a percentage of the average temperature.
Exact interpolation methods are indicated by RMSE and (RMSE ∕ Omean) values of zero.Accordingly, the most accurate interpolation methods are indicated by RMSE and (RMSE ∕ Omean) values closest to zero.It should be noted that for interpolation of temperature data, estimation error is unlikely to be zero) (.Hutchinson(2004) states that standard error of fitted surfaces should be approximately 10% for monthly mean temperature data when adequate networks are available.
Model efficiency (E) equals 1 when observations and estimations are in perfect agreement.Model efficiency can be less than zero when the model estimations are worse than using the average of observed temperature as an estimator.For high model efficiency, the mean square error (MSE) of the temperature estimations will need to be small relative to stander deviation of the observed temperature.
Interpolation results that indicate no bias have a bias statistic value of 1.That is, the average temperature estimate is equal to the average observed temperature.Bias values greater than one indicate that the estimated temperature is generally over estimated, while values less than one suggest that the interpolation method resulted in underestimation [10].

Discuses and results 1-Discuses results for mean maximum temperature
Table 2 shows the average error statistics for each of the three interpolation methods based on the climate data available.For these samples, when applying IDW, ordinary kriging, and Spline are found to perform comparably to each other.The Spline method has the highest RMSE.These three methods are producing the same results for the model efficiency.Ordinary kriging and IDW provide more accurate estimation than Spline method.More frequent occurrence of extreme error is observed with Spline interpolation.The root mean square error gave good results close to zero.
Figs.2-7, illustrated continuous surfaces for spatial interpolation methods to produce the estimation values in areas where there are no measurements.Figs.8-10 are comparisons of estimated and observed mean maximum temperature for nine climate stations lying south of Iraq.These figures represent the IDW, Spline, and ordinary kriging methods respectively which producing the behavior of estimated mean maximum temperature with the mean maximum observer temperature.The relation between estimation and observed mean max temperatres, the weakest correlation occurred (R 2 =0.119,R 2 =0.118) for these climate data.

2-Discuses results for mean minimum temperature
These IDW, Ordinary kriging, and Spline interpolation methods are used for mean minimum temperature to produce the best one between them.As illustrated in Table 3, the Spline method has the highest RMSE.These three methods are producing the highest accurate results for RMSE, the same results for model efficiency and the best results for the bias method.Ordinary kriging and IDW provide more accurate estimation than Spline method.More frequent occurrence of extreme error is observed with Spline interpolation.Also for root mean square error gave good results close to zero such as the results for max temperature.
The results of the bias for these three methods have the value of one, which producing that the average minimum temperature estimate is equal to average minimum temperature observed.