An intercomparison of observational precipitation data sets over Northwest India during winter

Abstract

Winter (DJF) precipitation over Northwest India (NWI) is very important for the cultivation of Rabi crops. Thus, an accurate estimation of high-resolution observations, evaluation of high-resolution numerical models, and understanding the local variability trends are essential. The objective of this study is to verify the quality of a new high spatial resolution (0.25° × 0.25°) gridded daily precipitation data set of India Meteorological Department (IMD1) over NWI during winter. An intercomparison with four existing precipitation data sets at 0.5° × 0.5° of IMD (IMD2), 1° × 1° of IMD (IMD3), 0.25° × 0.25° of APHRODITE (APRD1), and 0.5° × 0.5° of APHRODITE (APRD1) resolution during a common period of 1971–2003 is done. The evaluation of data quality of these five data sets against available 26 station observations is carried out, and the results clearly indicate that all the five data sets reasonably agreed with the station observation. However, the errors are relatively more in all the five data sets over Jammu and Kashmir-related four stations (Srinagar, Drass, Banihal top, and Dawar), while these errors are less in the other stations. It may be due to the lack of station observations over the region. The quality of IMD1 data set over NWI for winter precipitation is reasonably well than the other data sets. The intercomparison analysis suggests that the climatological mean, interannual variability, and coefficient of variation from IMD1 are similar with other data sets. Further, the analysis extended to the India meteorological subdivisions over the region. This analysis indicates overestimation in IMD3 and underestimation in APRD1 and APRD2 over Jammu and Kashmir, Himachal Pradesh, and NWI as a whole, whereas IMD2 is closer to IMD1. Moreover, all the five data sets are highly correlated (>0.5) among them at 99.9% confidence level for all subdivisions. It is remarkably noticed that multicategorical (light precipitation, moderate precipitation, heavy precipitation, and very heavy precipitation) skill score of accuracy (>0.8) for the four data sets against IMD1 is good for all the subdivisions as well as NWI and is more in IMD2. IMD1 performs well in capturing the relationships of winter precipitation with climate indices such as Nino 3.4 region sea surface temperature, Southern Oscillation Index, Arctic Oscillation, and North Atlantic Oscillation. The results conclude that IMD1 is useful to understand the variability trends at the local climate scale and its global teleconnections.

Appendices

Appendix I

1.1 Root mean square error

It is routinely used as the measure of the differences between model values and actually observed values, and it is generally called as residual or error of the model. The RMSE serves to aggregate the magnitudes of the errors in model for various times into a single measure of estimating power. The RMSE computed as

$$ \mathrm{RMSE}=\sqrt{\frac{\sum_{i=1}^{i= n}{\left({X}_i-{O}_i\right)}^2}{n}} $$

where X _i is the ith time estimated value of the method (IMD2, IMD3, APRD1, and APRD2).

O _i is the ith time value of actual observed (IMD1).

1.2 Mean bias

Mean bias indicates that the method is overestimated or underestimated or exactly matched with actual observed climatology. It is computed as

$$ MB=\overline{X}-\overline{O} $$

where $\overline{X}$ indicates the climatological mean value of the method (IMD2, IMD3, APRD1, and APRD2).

$\overline{O}$ indicates the climatological mean value of reference method (IMD1).

1.3 Modified mean bias

It provides a measure of the bias of the model (IMD2, IMD3, APRD1, and APRD2) with observation (IMD1) that performs symmetrically with respect to underprediction and overprediction and is bounded by the value −2 to +2. It is computed as

$$ \mathrm{MMB}=\frac{2}{n}{\sum}_{i=1}^{i= n}\left(\frac{X_i-{O}_i}{X_i+{O}_i}\right) $$

1.4 Fraction gross error

The fractional gross error also gives a measure of the overall error of the model (IMD2, IMD3, APRD1, and APRD2) with observation (IMD1), and it is bounded by the value 0 to 2. It is computed as

$$ \mathrm{FGE}=\frac{2}{n}{\sum}_{i=1}^{i= n}\left|\frac{X_i-{O}_i}{X_i+{O}_i}\right| $$

1.5 Index of agreement

It is a standardized measure of the degree of model (IMD2, IMD3, APRD1, and APRD2) error with observation (IMD1), and it ranges from 0 to 1 (Willmot 1981). Value “1” indicates a perfect agreement between estimated values of model and actual observation, and “0” represents for no agreement. The IOA represents the ratio between the mean square error and potential error. The potential error is the sum of the squared absolute values of the distances from the estimated values to the mean of actual observed values and distances from actual observed values to the mean actual observed value. The IOA detects additive and proportional differences in the observed and estimated means and variances. It computed as

$$ IOA=1-\left(\frac{\sum_{i=1}^{i= n}{\left({X}_i-{O}_i\right)}^2}{\sum_{i=1}^{i= n}\left(\left|{X}_i-\overline{O}\right|+\left|{O}_i-\overline{O}\right|\right)}\right) $$

1.6 Nash–Sutcliffe efficiency coefficient

It is generally used to assess the estimation power of the model (Nash and Sutcliffe 1970). In addition, it can be used to describe quantitatively the accuracy of the model. It is defined as

$$ E=1-\left(\frac{\sum_{i=1}^{i= n}{\left({O}_i-{X}_i\right)}^2}{\sum_{i=1}^{i= n}{\left({O}_i-\overline{O}\right)}^2}\right) $$

Nash–Sutcliffe efficiency skill score ranges from −∞ to 1. Value 1 indicates a perfect match between estimated values of model and actual observations. Whereas an NSEC less than zero (−∞ < NSEC < 0) occurs when the actual observed mean is a better predictor than the model.

1.7 Correlation coefficient

The correlation coefficient is a commonly used skill score for a measure of the strength and direction of the linear relationship between two variables. It is defined as

$$ \mathrm{CC}=\frac{\sum_{i=1}^{i= n}\left({X}_i-\overline{X}\right).\left({O}_i-\overline{O}\right)}{\sqrt{\sum_{i=1}^{i= n}{\left({X}_i-\overline{X}\right)}^2\cdot {\sum}_{i=1}^{i= n}{\left({O}_i-\overline{O}\right)}^2}} $$

Appendix II

1.1 Accuracy (ACC)

ACC indicates that the overall fraction of the forecasts was in the correct category; this skill score range is 0 to 1. Value 1 indicates perfect to match the all categories. ACC is computed as

$$ \mathrm{ACC}=\frac{1}{N}{\sum}_{i=1}^{i= k} n\left({F}_i,{O}_i\right) $$

1.2 Heidke skill scores (HSS)

Heidke skill scores compare the accuracy of the given forecast against the accuracy of a forecast of random chance (Heidke 1926; Mason 2003). This skill score range is from −∞ to 1. Value 1 represents a perfect skill score. A negative HSS indicates that a forecast is worse than a random-based/generated forecast. HSS is defined as

$$ \mathrm{HSS}=\frac{\frac{1}{N}{\sum}_{i=1}^{i= k} n\left({F}_i,{O}_i\right)-\frac{1}{N^2}{\sum}_{i=1}^{i= k} N\left({F}_i\right) N\left({O}_i\right)}{1-\frac{1}{N^2}{\sum}_{i=1}^{i= k} N\left({F}_i\right) N\left({O}_i\right)} $$

1.3 Hanssen and Kuipers discriminant (HK)

Hanssen and Kuipers discriminant is nearly similar to Heidke skill score, except that in the denominator, the fraction of correct forecasts due to random chance is for an unbiased forecast (Wilks 2011). This skill score range from −1 to 1. Value 0 indicates no skill, and 1 represents a perfect agreement. It is computed as

$$ \mathrm{HK}=\frac{\frac{1}{N}{\sum}_{i=1}^{i= k} n\left({F}_i,{O}_i\right)-\frac{1}{N^2}{\sum}_{i=1}^{i= k} N\left({F}_i\right) N\left({O}_i\right)}{1-\frac{1}{N^2}{\sum}_{i=1}^{i= k}{\left( N\left({O}_i\right)\right)}^2} $$