| dc.description.abstract | The shifting patterns of weather and climate in Jakarta, particularly in terms
of rainfall and air temperature, increasingly reflect uncertainty that has a tangible
impact on the growing risk of hydrometeorological disasters such as floods and
droughts. This situation is further exacerbated by global phenomena such as the
warming of average surface temperatures, which influence regional atmospheric
and hydrological systems. Investigating key climate variables has therefore become
essential to better understand the dynamics of these changes and to design effective
mitigation strategies. Most analytical approaches in Indonesia still rely on the
assumption that climate data are stationary, whereas empirical evidence and long
term observations indicate changes in trends and statistical fluctuations that can no
longer be ignored. Consequently, it is necessary to develop statistical models
capable of flexibly capturing the evolving dependence structures between climate
variables, under both normal and extreme conditions, in order to predict and
understand the continuously shifting hydrometeorological trends.
This study utilizes annual time series data from 1864 to 2020, obtained from
KMNI and BMKG Kemayoran observation stations. The dataset consists of rainfall
and air temperature measurements in Jakarta, analyzed as two primary components
shaping the local climate. The initial step involved univariate modeling to
determine the most suitable probability distribution for each variable. Stationarity
testing using the KPSS method indicated that both datasets were non-stationary,
leading to the adoption of models with time-varying parameters. Based on
univariate estimation results, the lognormal distribution was deemed appropriate
for modeling rainfall due to its asymmetry and tendency toward extremes, while the
Generalized Extreme Value (GEV) distribution was applied to air temperature,
given its suitability for capturing tail behavior in extreme data. Further evaluation
was carried out by assessing the cumulative distribution function (CDF) against the
uniform distribution using the Kolmogorov–Smirnov (K-S) test and Q–Q plots. The
results confirmed that the data transformations were appropriate for use in copula
construction, providing a sound basis for developing hydrometeorological trend
models that account for the dynamic relationships between variables.
The joint behavior of rainfall and air temperature was modeled using bivariate
distribution approaches through one-parameter Archimedean copulas, namely the
Clayton, Gumbel, and Frank copulas. These were selected for their flexibility in
capturing characteristic dependencies in climate data, such as strong lower-tail
dependence (Clayton), upper-tail dependence (Gumbel), and symmetric
dependence (Frank). Parameter estimation was performed using three main
methods: the fminsearch optimization algorithm, Markov Chain Monte Carlo
(MCMC) simulation, and a combination of both, to obtain stable and robust
parameter estimates. The models were developed in two forms: stationary (with
time-invariant parameters) and non-stationary (with parameters that vary linearly
over time), in order to capture long-term dynamics in variable relationships and
more accurately detect hydrometeorological trends.
The analysis revealed that the best-performing model was the non-stationary
Clayton copula estimated using MCMC simulation. This model produced the
lowest values of Akaike Information Criterion (AIC) and Mean Absolute
Percentage Error (MAPE), indicating the best fit between the modeled dependence
structure and the observed data. Additionally, the Clayton copula demonstrated the
ability to capture extreme lower-tail dependence, which is relevant for events such
as droughts accompanied by low temperatures—an important phenomenon often
overlooked by conventional models. The estimation results also showed that the
copula parameters varied significantly over time, supporting the hypothesis that the
relationships between climate variables are not constant but dynamically evolve in
response to global and regional climate pressures.
Model visualization was carried out using contour plots of the joint
distribution, which illustrated how the patterns shifted over time. These shifts
indicated not only an increase in the median values of rainfall and air temperature
but also suggested a more complex dependency structure between the two variables.
The distribution was observed to shift toward higher values in both variables,
reflecting simultaneous trends of warming and intensified rainfall in Jakarta. Such
patterns characterize the emergence of new hydrometeorological trends distinct
from previous periods and are essential to interpret within the framework of climate
adaptation policies.
Overall, the time-varying bivariate copula approach, particularly the non
stationary Clayton copula with MCMC-estimated parameters, proves effective in
capturing the dynamic dependence between rainfall and air temperature in Jakarta.
This model not only identifies complex statistical relationships but also offers visual
and quantitative evidence that climate change is indeed occurring in urban areas
like Jakarta and must be addressed through appropriate scientific methods. Its
ability to map the direction and strength of inter-variable relationships over time
makes it a valuable tool for analyzing and projecting future hydrometeorological
trends. The study contributes to the development of an applicable statistical
framework for climate adaptation and mitigation planning, especially in regions
facing intense urbanization and climate variability. | |
