Tanzania is a tropical country in East Africa located just south of the equator between latitudes 0˚ and 12˚S and longitudes 28˚E and 42˚E. It also borders the Indian Ocean on its eastern side, and three great lakes: Lake Victoria in the Northwestern part, Lake Tanganyika aligning in the West and lake Nyasa in the South. It is also home to many rivers, hills, Serengeti plains and Ngorongoro crater. It is located to the east of the Congo Basin and the Congo Rainforest ( Figure 1 ).

The country features complex topographical landscape including the highest point in Africa, Mount Kilimanjaro, which stands at 5895 meters.

Tanzania experiences two distinct climatic seasons which are the dry and wet seasons. The wet is classified into two distinct seasons: the long rains (Masika) from March to May (MAM) and the short rains (Vuli) from October to December (OND). Other months feature lower rainfall and generally cooler temperatures, particularly in the highlands and are classified as dry seasons. January and February are often the hottest months partly because of rainfall shortage while receiving high solar insolation over large part of Tanzania [5] [27] [28] . The diverse geography and topography shown in Figure 1 , create distinct microclimates and climate patterns. Indian Ocean in the eastern part plays a crucial role in regulating the climate in the region. It is found that the warmer (cooler) than normal of East Africa-SST tend to influence the climate by suppressing (enhancing) OND rainfall in Tanzania [27] . Tanzania’s climate variability is significantly influenced by Southern Hemisphere subtropical high-pressure systems, particularly the MH and the SH. The variability in these systems, along with the Indian Ocean Monsoon, Equatorial Low-Pressure System, East African Low-Level Jet (EALLJ), and South Indian Ocean cyclones, also impacts the region’s westerly and easterly winds [20] [24] [28] [29] .

The climatology map of Tanzania in Figure 2(a) shows that distribution of 2020 annual and OND T2m depends on the latitude, altitude, proximity to the Indian ocean and the presence of large water bodies such as lakes Victoria, Tanganyika and Nyasa. During OND season, the sun is on its way to the south, so southern parts gradually receive more solar insolation becoming warmer than the northern parts surrounding Lake Victoria ( Figure 2(c) ). Also, from the time series of the daily average T2m ( Figure 2(b) ), OND is relatively higher than other months. It can be observed that, Coastal areas are relatively warmer than the rest of the country due to the influence of Indian ocean temperature moderation. ISV of temperature along the coast is expected to be moderated by the influence of the sea surface temperature. Figure 2(d) shows the presence of oscillation in the OND season T2m climatic time series calculated from 40-year data (1979-2022).

The station data consisting of daily Maximum and minimum temperature (˚C) from 18 stations from years 2018-2022 were collected from Tanzania Meteorological Authority (TMA). For each station, the daily mean surface temperature (T2m) was calculated as the average of the maximum and minimum temperatures. The data were used as the primary data set for identification of temperature fluctuation period. The spatial distribution of the stations which are used in this study is illustrated in Figure 1 . For further spatial-temporal analysis, it utilizes data from the NCEP/DOE Reanalysis 2 (R2) Project [30] . The dataset is available in NetCDF format and has temporal Coverage daily values derived from years 1979/01 to 2024/08, Spatial Coverage 2.5-degree latitude × 2.5-degree longitude global grid (144 × 73) 90N - 90S, 0E - 357.5E. It covers 17 pressure levels. Furthermore, this dataset has been applied by other researchers to examine intraseasonal variability of temperature over different regions hence it is appropriate for this study [5] [11] [19] [20] [22] [31] - [33] .

Temporal analysis seeks to identify patterns such as trends, seasonality, and cyclic behavior in the observed data. This helps to describe the systematic components of the time series [34] . Cyclical components exist when data exhibit rises and falls that are not necessarily of fixed period. The average length of cycles is longer than the length of a seasonal pattern. In this study only one season during OND months is analyzed, which limits the influence of annual cycles in the time series. OND seasonal departures were calculated by subtracting the OND mean, highlighting fluctuations around the mean season which gives insight of the presence of ISV in the time series (e.g. biweekly, 30 to 60 days) [35] . The observed time series (seasonal departures) is smoothed by using two-sided averaging technique (centered moving average) shown in Equation (1). This helps to clearly view the seasonal patterns by removing the noises of higher frequencies [36] .

$\hat{T}=\frac{Y_{t-2}+Y_{t-1}+Y_t+Y_{t+1}+Y_{t+2}}{5}$ (1)

where: $\hat{T}$ is the smoothed value at t.

$Y_{t-2}$, $Y_{t-1}$, $Y_1$, $Y_{t+1}$, $Y_{t+2}$, are values at times t − 2, t − 1, t, t + 1 and t + 2 respectively.

Long-term trends are removed by fitting a polynomial regression model to the smoothed data to capture the remaining and then subtracted this polynomial trend from the smoothed data as shown in Equation (2).

$X_t=a_0+a_{1}t+a_2{t}^2+a_3{t}^3+e_t$ (2)

where: $X_t$ is the climatic variable (temperature) t is time, $a_0{a}_1{a}_2$ and $a_3$ are coefficients to be estimated and $e$ is the error term.

The power spectrum method was used to transform time series discussed in previous section to a Period Domain. In this method, Fourier Transform was used to convert the time series data to a frequency (period) domain and compute the power spectrum. Dominant frequency (period) is identified by assessing the level of significance for different cycle periods and selecting the pattern which passes 95% confidence interval. Most studies of ISV of climate in Tanzania use pre-determined ISO indices such as MJO missing fast moving atmospheric patterns such as biweekly patterns. Power spectrum is a powerful method successfully used in many ISVs of climate researches [7] [12] [36] [37] . Unlike other techniques, such as simple trend analysis or autocorrelation, the power spectrum reveals how much variance in the data is associated with different frequency components. This is particularly useful for analyzing periodic or oscillatory behaviors, like intraseasonal climate variations, as it allows us to pinpoint specific periods of variability (e.g., biweekly or monthly cycles). Additionally, the power spectrum method is robust to noise, especially when combined with smoothing and confidence interval estimation, making it well-suited for detecting underlying patterns in complex, noisy climate data [38] .

Based on the results of the power spectrum analysis, a 10 - 25-day band-filtering was applied to the time series data using the Lanczos filtering method, as described by Yang and Li [11] to extract the biweekly component. Lanczos filtering is a digital signal processing technique that utilizes a mathematical approach based on the Lanczos kernel to reduce noise and extract meaningful signals from data. This method is particularly effective in mitigating Gibbs oscillations, which can distort the representation of signals when using traditional Fourier methods. The Lanczos filter is characterized by its ability to maintain a balance between low-frequency preservation and high-frequency rejection, making it a preferred choice for various applications in signal processing and data analysis [39] .

This method is useful for isolating the dominant periodicity of interest from the spectral analysis results. It has been used successfully in many other studies, including those by Yang and Li [40] , Wen et al. [41] [42] , Wang et al. [43] , and Krishnamurti and Ardanuy [6] . It uses a linear relationship to transform the raw data sequence $x_t$ into a filtered data sequence $y_t$ as shown in Equation (3) and Equation (4).

$y_t=\underset{k=-n}{\overset{n}{{\displaystyle \sum }}}{w}_k{x}_{t+k}$ (3)

where; $y_t$ is the bandpass filtered output at time t, $x_{t+k}$ is the input time series at time t + k and $w_k$ are smoothed weights which for bandpass filtering, is written as

$w_k=\left(\frac{\sin 2\text{π}{f}_{c2}k}{\text{π}k}-\frac{\sin 2\text{π}{f}_{c1}k}{\text{π}k}\right)\frac{\sin \text{π}k/n}{\text{π}k/n}$ (4)

$K=-n,\cdots ,0,\cdots$

This method involved processing a gridded T2m dataset from NCEP/DOE Reanalysis 2 (R2) by using Python data analysis tool. A shapefile of Tanzania’s administrative boundaries was used to clip the data to the study area. Lag phases were defined based on key dates ( Table 1 ), and mean temperatures for each phase were calculated by averaging T2m data from selected dates. Warm events are considered as days with larger or equal to one standard deviation (> or = 1std) and the average of the days with peak values are considered as day 0 (lag 0). Table 1 shows the peak days dates and their corresponding observed positive peak values. The results were visualized in a 3 × 3 grid of subplots with contour plots and a diverging colormap to highlight the seasonal departures. By combining spatial and temporal dimensions, this methodology offers a powerful tool for understanding complex ISV of T2m in Tanzania, as demonstrated in the study by Bantzer and Wallace [44] .

Filtered OND T2m, wind and geopotential height (hgt) maps are plotted in the interval of 2 days before and after day 0. Day –n and day n refer to n days before and after the peak temperature days (day 0), respectively. In the total 92 days during the OND, 2020, several peaks are chosen as the day 0 of the warm phase of ISV temperature cases in this study ( Table 1 ).

Based on peak days average shown on Table 1 , the composite time evolution of observed T2m ( Figure 3 ) is used as the basis for the analysis of the composite time evolution maps using the gridded data. First T2m gridded data is filtered using a band-pass filter to capture oscillations with a 10 to 25-day period for plotting a spatial maps time evolution then plots are analyzed to confirm whether the ISV of temperature prevails and link it with the atmospheric circulation patterns associated with it. The method has been used by several researchers to study ISV of climate [11] [15] [36] [37] [45] .

Negative peak events ( Table 2 ) are also used to confirm the oscillation observed by using cold peak events. Overall, composite analysis is an effective tool for studying intraseasonal variability because it focuses on event-based analysis, enhances signal clarity, and provides insights into recurrent climate dynamics that may otherwise be obscured in raw, unaveraged data.

To test the significance level of variability, Student’s t-test method implemented by python analysis software is used to assess the statistical significance at 95% confidence level (α = 0.05) according to the Equation (5).

$t=\frac{\overline{x_1}-\overline{x_2}}{\sqrt{\frac{\left(n_1-1\right)S_1^2+\left(n_2-1\right)S_2^2}{n_1+n_2-2}\left(\frac{1}{n_1}+\frac{1}{n_2}\right)}}$ (5)

where, $n_1$ and $n_2$ are sample sizes of the two groups, $S_1^2$ and $S_2^2$ are the sample variances of the two groups. This is used to test the significance of climate variability of the 10 - 25-day period filtered mean peak seasonal departures. The method has been successfully used by several researchers such as [24] [37] [45] [46] .

Analysis of the Time series of the Tanzania field mean shown in Figure 4(a) and the separate stations in Figure 4(c) shows a similar pattern of periodic oscillation. This implies that the field mean data is a good representation of individual T2m station data. This visualization highlights temperature deviations from the seasonal norm, providing insights into intraseasonal temperature changes across the OND season.

Through the power spectrum method, time series patterns observed in Figure 4(a) transformed into period domain as shown in Figure 4(b) and Figure 4(d) . The plot reveals that the power spectral density is concentrated within the 10- to 25-day period, which surpasses the 95% confidence interval, indicating significant variance contributions at these intraseasonal timescales

Based on the results of power spectrum analysis, the 10 - 25 days period component of the observation data is filtered and plotted as shown in Figure 5 . Frequence band pass filtering with 95% confidence interval applied on temperature anomaly data based on lanczos filtering method shows the periodic patterns shown in Figure 5 .

To analyze the T2m composite spatial-temporal evolution maps, Figure 6 is plotted the same way as in Figure 3 by using 10 - 25 days filtered NCEP II reanalysis gridded data. The aim is to analyze the T2m time evolution over the study area after every 2 days starting from 8 days before the peak, named as lag negative 8 (−8 day) to 8 days after peak day, termed as lag positive 8 (+8 day) to complete a cycle of 16 days. Figure 6(a) shows the composite time evolution plotted by using day 0 (lag 0) as the average warm peak date while other lag days are plotted at an interval of 2 days before and after peak day (lag 0). Likewise, Figure 6(b) illustrates the composite time evolution of the cold peak days. To test the significance of the variability of the T2m over Tanzania, t-test analysis for warm and cold peaks are as illustrated in Figure 6(c) and Figure 6(d) respectively.

To observe the atmospheric circulations associated with the illustrated T2m patterns over Tanzania, broader area composite time evolution is shown in Figure 7 . The wind circulation is plotted from 10 - 25 days period of filtered wind data. The background shaded region represents filtered T2m over the broader area.

The region encircled in green shows the anomalous cyclonic flow while purple encircles the anomalous anticyclonic flow ( Figure 7 ). Figure 8 shows the two distinct phases which are the cold phase in Figure 8(a) and the warm phase in Figure 8(b) . Figure 8(c) is the illustration of the significance test of the wind variability.

The use of streamlines in plotting wind patterns shown in Figure 8 facilitates the clear view of the link between the wind patterns over Tanzania and the atmospheric circulation systems based on the broader area specifically the subtropical high systems in the southern hemisphere.

After analyzing wind systems, the link between the ISV of T2m over Tanzania and the variability of subtropical high-pressure systems in the Southern Hemisphere was established. The composite evolution of the 10 - 20 days period geopotential height, as shown in Figure 9 , further illustrates this relationship.

The straight line with arrows shown in Figure 9 illustrates the shifting of the geopotential height systems in the composite time evolution lag days. The red arrowed line represents the shifting of anomalous higher geopotential height, while the green line represents the shifting of low geopotential systems every 2 days.