Trend Analysis of Air Temperature in the Federal District of Brazil: 1980–2010
Abstract
:1. Introduction
2. Materials and Methods
Data Set Analysis
- T = total number of groups with identical symbols.
- H0 = there is no trend;
- H1 = there is a trend.
3. Results
4. Discussion
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Step 1. | The linear trend b of series Xt estimated by the Theil–Sen method is calculated. If b is “close” to zero, then it is assumed that there is no trend and the procedure ends. |
Step 2 | If b is not “close” to zero, a linear trend Tt in series Xt is assumed and the trend is removed from it: X’t = Xt − Tt = Xt − bt |
Step 3 | Considering the autoregressive model AR (1), the serial correlation coefficient r1 of the series (without trend) X’t is calculated and the autocorrelation AR (1) is removed from it: Y’t = X’t − r1 X’t−1 |
Step 4 | Series Y’t, which is now “clean”, without a trend Tt or AR (1) autocorrelation, is “pasted” to the trend to be identified by the Mann–Kendall test: Yt = Y’t + Tt In this way, Yt preserves its true trend and is not influenced by the effects of autocorrelation. |
Step 5: | The Mann–Kendall test is applied to series Yt. |
Maximum temperature | CNPH | FAL | CINDACTA | INMET | CPAC | |
N | 372 | 372 | 372 | 372 | 372 | |
Min | 22.4 | 24.33 | 26.8 | 23.35 | 23.97 | |
Max | 33.2 | 38.45 | 37.3 | 30.9 | 32.67 | |
Mean | 2.850457 | 2.865693 | 3.089194 | 2.661524 | 2.789621 | |
Std. error | 0.07870086 | 0.1066252 | 0.09394739 | 0.06954393 | 0.07500937 | |
Variance | 2.304103 | 3.001398 | 31.774 | 1.799125 | 2.093023 | |
Stand. Dev | 1.517927 | 1.732454 | 1.782526 | 1.341315 | 1.446728 | |
Median | 28.4 | 28.415 | 30.8 | 26.585 | 27.8 | |
25th percentile | 27.6 | 27.435 | 29.6 | 25.7225 | 26.9425 | |
75th percentile | 29.4 | 29.7 | 32 | 27.375 | 28.7075 | |
Skewness | 0.1657374 | 0.9238805 | 0.3261668 | 0.4618178 | 0.4384937 | |
Kurtosis | 0.9266567 | 3.26823 | −0.1142808 | 0.3999233 | 0.6199819 | |
Geom. mean | 28.4643 | 28.60623 | 30.84111 | 26.58194 | 27.85921 | |
Coeff. var | 5.325207 | 6.045498 | 5.770198 | 5.039649 | 5.186111 | |
Average temperature | CNPH | FAL | CINDACTA | INMET | CPAC | |
N | 372 | 372 | 372 | 372 | 372 | |
Min | 18.7 | 16.5 | 16.24403 | 16.97 | 18.58 | |
Max | 27 | 25.375 | 25.05969 | 24.76 | 25.42 | |
Mean | 2.305591 | 2.113223 | 21.439 | 2.102269 | 2.190777 | |
Std. error | 0.07048884 | 0.1133258 | 0.08263705 | 0.06855809 | 0.06728182 | |
Variance | 1.848348 | 3.390484 | 2.458398 | 1.748479 | 1.683986 | |
Stand. dev | 13.5954 | 18.41327 | 15.67928 | 13.22301 | 12.97685 | |
Median | 23.1 | 21.63 | 21.74049 | 21.18 | 22.075 | |
25th percentile | 22.3 | 19.825 | 20.57064 | 20.24 | 21.195 | |
75th percentile | 23.9 | 22.45 | 22.53285 | 21.84 | 22.7825 | |
Skewness | −0.1450918 | −0.536335 | −0.603428 | −0.3672645 | −0.2616349 | |
Kurtosis | 0.6940948 | −0.441302 | 0.127792 | 0.203304 | −0.0552102 | |
Geom. mean | 23.01548 | 21.04918 | 21.37971 | 20.98035 | 21.86888 | |
Coeff. var | 5.896706 | 8.713355 | 7.313438 | 6.289874 | 59.234 | |
Minimum temperature | CNPH | FAL | CINDACTA | INMET | CPAC | |
N | 372 | 372 | 372 | 372 | 372 | |
Min | 11.1 | 1.8 | 1.9 | 10.92 | 10.75 | |
Max | 22.9 | 22.38 | 19.7 | 19.73 | 19.43 | |
Mean | 16.8628 | 13.80871 | 12.89667 | 16.75196 | 16.49371 | |
Std. error | 0.09772559 | 0.2025824 | 0.1800133 | 0.09051469 | 0.09812114 | |
Variance | 3.552708 | 10.83446 | 11.66573 | 3.047762 | 3.581526 | |
Stand. dev | 1.884863 | 3.291574 | 3.415513 | 1.745784 | 1.892492 | |
Median | 17.5 | 14.83 | 13.8 | 17.49 | 17.255 | |
25th percentile | 15.425 | 11.2 | 10.2 | 153.675 | 15.12 | |
75th percentile | 18.2 | 16.2 | 15.7 | 180.575 | 17.93 | |
Skewness | −0.652321 | −0.686684 | −0.56908 | −0.8709872 | −0.8232476 | |
Kurtosis | −0.2157347 | 0.048029 | −0.4952163 | −0.2862008 | −0.483233 | |
Geom. mean | 16.75096 | 13.31522 | 12.33696 | 16.65447 | 16.37693 | |
Coeff. var | 11.17764 | 23.83694 | 26.48369 | 10.42137 | 11.47402 |
Test (p-Value) | Step 1 | Test (p-Value) | Step 2 | ||||
---|---|---|---|---|---|---|---|
Temperature | Station | Wald–Wolfowitz | Cox–Stuart | Mann–Kendall | Is There a Trend? | MK-Adjusted | Is There a Trend? |
Minimum | CINDACTA | 2.0062 × 10−24 | 0.057615976 | 0.017756332 | yes | 0.2510 | no |
FAL | 1.69571 × 10−23 | 0.001414448 | 0.248676166 | yes | 0.0948 | no | |
INMET | 4.7 × 10−29 | 0.045721123 | 1.415 × 10−7 | yes | 0.3127 | no | |
CPAC | 0 | 0.081699116 | 0.010615543 | yes | 0.8776 | no | |
CNPH | 7 × 10−30 | 0.106234147 | 0.009305695 | yes | 0.1907 | no | |
Average | CINDACTA | 2.43843 × 10−15 | 2.2172 × 10−6 | 0.000200051 | yes | 0.0948 | no |
FAL | 2.25623 × 10−20 | 3.7 × 10−9 | 0.004867564 | yes | 0.4656 | no | |
INMET | 3.91319 × 10−13 | 0.003976863 | 2.0376 × 10−6 | yes | 0.0131 | no | |
CPAC | 9.8304 × 10−17 | 0.412983814 | 0.184920311 | no | 0.1684 | no | |
CNPH | 2.10328 × 10−11 | 0.00072815 | 0.001942255 | yes | 0.2310 | yes | |
Maximum | CINDACTA | 2.46062 × 10−11 | 0.183556922 | 0.365201205 | no | 0.5374 | no |
FAL | 5.75176 × 10−8 | 0.011371634 | 0.309852392 | yes | 0.2511 | no | |
INMET | 3.7282 × 10−8 | 0.0002667 | 0.000222662 | yes | 0.0033 | yes | |
CPAC | 1.53129 × 10−7 | 1.26909 × 10−5 | 4.663 × 10−7 | yes | 0.0014 | yes | |
CNPH | 5.69459 × 10−9 | 0.000316394 | 1.68551 × 10−5 | yes | 0.0198 | yes |
Station | Altitude | Is There a Trend? | What Is the Trend? | Trend Percentage * | ||
---|---|---|---|---|---|---|
Tmax | Tav | Tmin | ||||
CINDACTA | 1055 | yes | Increase | 0.1% | 3% | 1.5% |
FAL | 1080 | yes | decrease | 0.2% | 2% | 1% |
INMET | 1160 | yes | Increase | 4% | 6% | 3% |
CPAC | 1000 | yes | Increase | 0.7% | 0.1% | 0.1% |
CNPH | 1000 | yes | Increase | 5% | 2% | 1% |
Station | Area of Influence | Urban Area 1981 | Growth in 1981–2010 | Growth Rate | Urban Area in 2010 | |||
---|---|---|---|---|---|---|---|---|
Name | km2 | km2 | % | km2 | % | % | km2 | % |
CNPH | 29 | 0.12 | 0.43 | 2.96 | 10.20 | 2330.70 | 3.08 | 10.64 |
INMET | 29 | 11.65 | 40.17 | 4.69 | 16.17 | 40.25 | 16.34 | 56.34 |
CPAC | 29 | 0.62 | 2.13 | 1.75 | 6.03 | 282.25 | 2.37 | 8.17 |
CINDACTA | 29 | 11.94 | 41.17 | 4.33 | 14.93 | 36.26 | 16.27 | 56.10 |
FAL | 29 | 3.13 | 10.79 | 1.95 | 6.72 | 62.30 | 5.08 | 17.51 |
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Steinke, V.A.; Martins Palhares de Melo, L.A.; Luiz Melo, M.; Rodrigues da Franca, R.; Luna Lucena, R.; Torres Steinke, E. Trend Analysis of Air Temperature in the Federal District of Brazil: 1980–2010. Climate 2020, 8, 89. https://doi.org/10.3390/cli8080089
Steinke VA, Martins Palhares de Melo LA, Luiz Melo M, Rodrigues da Franca R, Luna Lucena R, Torres Steinke E. Trend Analysis of Air Temperature in the Federal District of Brazil: 1980–2010. Climate. 2020; 8(8):89. https://doi.org/10.3390/cli8080089
Chicago/Turabian StyleSteinke, Valdir Adilson, Luis Alberto Martins Palhares de Melo, Mamedes Luiz Melo, Rafael Rodrigues da Franca, Rebecca Luna Lucena, and Ercilia Torres Steinke. 2020. "Trend Analysis of Air Temperature in the Federal District of Brazil: 1980–2010" Climate 8, no. 8: 89. https://doi.org/10.3390/cli8080089