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Based on the detrended fluctuation analysis (DFA) method, scaling behaviors of the daily outgoing longwave radiation (OLR) from 1979 to 2015 over the Tibetan Plateau (TP) and the Indian Monsoon Region (IMR) are analyzed. The results show that there is long-term memory for the OLR time series over the TP and IMR. The long-range memory behaviors of OLR over TP are stronger than those over IMR. The averaged values of the scaling exponents over TP and IMR are 0.71 and 0.64; the maximum values in the two regions are 0.81 and 0.75; the minimum values are 0.59 and 0.58. The maximum frequency counts for scaling exponents occur in the range of 0.625 and 0.675 both in TP and in IMR. The spatial distribution of the scaling exponents of the OLR sequence is closely related to the conditions of climatic high cloud cover in the two areas. The high cloud cover over TP is obviously less than that of IMR. In addition, the scaling behaviors of OLR over TP and IMR are caused by the fractal characteristics of time series, which is further proved by randomly disrupting the time series to remove trends and correlation.

As is known to all, the change of a climate system has the self-memory characteristic. This means that the past climate has a long-term effect on the variational trend of the current and future climate system. Long-range memory (LRM), which is also called the long-range correlation (LRC) or long-term persistence, has been found in many observations, such as daily temperature records [

OLR is the energy radiating from the earth to external space as infrared radiation. It has a close relationship with earth-atmosphere radiation budget [

In this study, we investigate the long-range correlation of the OLR from 1979 to 2015 over the Tibetan Plateau (TP) and the Indian Monsoon Region (IMR) and compare the differences between them. The results indicate that the variation of OLR is not random but demonstrate obvious LRC. This paper is organized as follows. In Section

The daily OLR time series between 1979 and 2015 are downloaded from the website of the National Oceanic and Atmospheric Administration (

The generalized DFA method, which was introduced by Peng et al. [

We first remove the annual cycle from the raw data

Next, we divide the series

The detrended fluctuation function is obtained with the arithmetic mean of the variance in all segments:

If the fluctuation function

Two grid points, (95°E, 35°N) and (97.5°E, 12.5°N), located in TP and IMR, respectively, are chosen randomly to analyze the scaling behaviors of OLR time series. The temporal evolution of OLR anomaly and cumulative deviation during the period from 1979 to 2015 is shown in Figure

The anomaly and cumulative deviation of OLR in TP (a, b) and IMR (c, d). The black and red line in (b) and (d) represent the original and shuffled time series, respectively.

The double log plots of power-law relationship between the detrended variability

The double log plots of the power-law relationship between the detrended variability

In order to illustrate the LRC of the OLR sequence over TP and IMR in an overall manner, the spatial distribution of the scaling exponents is shown in Figure

The geographical distribution of the scaling exponents of the daily OLR sequence over TP and IMR.

The spatial distribution of total cloud over TP and IMR.

In order to further describe the differences between the two regions, the frequency distribution of the scaling exponents of OLR is given in Figure

The main parameters of scaling exponents of the OLR sequence on TP and IMR.

DFA2 | Minimum | Maximum | Average | Standard deviation |
---|---|---|---|---|

TP | 0.59 | 0.81 | 0.71 | 0.042 |

IMR | 0.58 | 0.75 | 0.64 | 0.036 |

Shuffled_TP | 0.46 | 0.58 | 0.50 | 0.016 |

Shuffled_IMR | 0.48 | 0.56 | 0.50 | 0.012 |

The frequency distribution of the scaling exponents of OLR over TP (a) and IMR (b).

In this paper, the DFA method is used to analyze the long-term memory characteristic over TP and IMR. The two grid points, (95°E, 35°N) and (97.5°E, 12.5°N), located in TP and IMR, respectively, are chosen randomly to analyze the scaling behaviors of OLR time series by using the different orders of DFA. The results present the notion that the slope is approximately linear for the four different orders of DFA, which means that there exist obviously similar scaling behaviors by using the different orders of DFA. Among them, DFA2 can remove unexpected trends, and therefore it is used to calculate LRC over the two regions. Generally, the scaling exponents in IMR are smaller than those of TP, which indicates stronger long-term memory characteristic for TP. Meanwhile, the scaling exponents of OLR have a decreasing trend from west to east over TP. The maximum frequency counts of scaling exponents occur in the range of 0.67 and 0.69 both in TP and in IMR. The spatial distribution feature of the scaling exponents of the OLR sequence in the two regions is mainly affected by that of the cloud cover. The high cloud cover over TP is obviously less than that of IMR. For TP region, the cover of cloud increases from west to east, and consequently the LRM becomes weaker from west to east over TP. In the Indian Ocean region, there exists a strong convection, which leads to larger high cloud cover. The scaling exponents of shuffled OLR records in the two places are near 0.5, which illustrates that LRC behaviors of OLR in the two regions are caused by the fractal characteristics of time series.

The authors declare that they have no conflicts of interest.

This study was funded by the National Natural Science Foundation of China (nos. 41571044 and 41001283) and by the Climate Change Special Fund of the China Meteorological Administration (no. CCSF201716).