Daily Rainfall Occurrence Research Articles

Statistical downscaling model for future projection of daily IDF relationship by Markov chain and kernel density estimator

ABSTRACT Changes in climate might have a significant impact on rainfall characteristics, including extreme rainfall. This study aims to project the future daily rainfall, preserving most of the rainfall characteristics, including extreme rainfall incorporating climate changes. This paper presents two hybrid semi-parametric statistical downscaling models for future projection of IDF curves. The precipitation flux from seven scenarios of ten GCMs and observed daily rainfall data are considered as predictors and predictand variables, respectively. At site, daily rainfall occurrence is modeled using a two-state first-order Markov chain. Rainfall amounts on each wet day are modelled using a univariate nonparametric kernel density estimator. Two types of amount generation models are presented in this study. The bounded model (KDE-SP) is developed, considering the support for the kernel distribution as positive. In the unbounded model (KDE-Ext), the wet days are reclassified as extreme and non-extreme rainy days. A significant increasing trend can be observed in the future projected intensity–duration–frequency relationships. The maximum increment using empirical distribution is observed as 93.21 and 80.93% on a 5-year return period in the far future for the SSP5-8.5 scenario, using KDE-Ext and KDE-SP models, respectively. Although both methods show similar results, the KDE-Ext model performs better in simulating extreme rainfall.

Future Scenarios of Design Rainfall Due to Upcoming Climate Changes in NSW, Australia

The occurrence of rainfall is significantly affected by climate change around the world. While in some places this is likely to result in increases in rainfall, both winter and summer rainfall in most parts of New South Wales (NSW), Australia are projected to decrease considerably due to climate change. This has the potential to impact on a range of hydraulic and hydrologic design considerations for water engineers, such as the design and construction of stormwater management systems. These systems are currently planned based on past extreme rain event data, and changes in extreme rainfall amounts due to climate change could lead to systems being seriously undersized (if extreme precipitation events become more common and/or higher in magnitude) or oversized (if extreme rainfall events become less frequent or decrease in magnitude). Both outcomes would have potentially serious consequences. Consequently, safe, efficient, and cost-effective urban drainage system design requires the consideration of impacts arising from climate change on the approximation of design rainfall. This study examines the impacts of climate change on the probability of occurrence of daily extreme rainfall in New South Wales (NSW), Australia. The analysis was performed for 29 selected meteorological stations located across NSW. Future design rainfall in this research was determined from the projected rainfall for different time periods (2020 to 2039, 2040 to 2059, 2060 to 2079, and 2080 to 2099). The results of this study show that design rainfall for the standard return periods was, in most cases, lower than that derived employing the design rainfall obtained from the Australian Bureau of Meteorology (BoM). While most of the analysed meteorological stations showed significantly different outcomes using the climate change scenario data, this varied considerably between stations and different time periods. This suggests that more work needs to be performed at the local scale to incorporate climate change predicted rainfall data into future stormwater system designs to ensure the best outcomes.

Comparison of Future Design Rainfall with Current Design Rainfall: A Case Study in New South Wales, Australia

Climate change impacts have the potential to alter the design rainfall estimates around the world. Decreasing trends in the summer and winter rainfall in New South Wales (NSW), Australia have already been observed due to climate variability and change. The derivation of design rainfall from historical rainfall, which is required for the design of stormwater management infrastructure, may be ineffective and costly. It is essential to consider climate change impacts in estimating design rainfall for the successful design of stormwater management infrastructure. In this study, the probability of the occurrence of daily extreme rainfall has been assessed under climate change conditions. The assessment was performed using data from 29 meteorological stations in NSW, Australia. For the evaluation of future design rainfall, the probability of the occurrence of extreme rainfall for different recurrence intervals was developed from daily extreme rainfall for the periods of 2020 to 2099 and compared with the current Australian Bureau of Meteorology (BoM) design rainfall estimates. The historical mean extreme rainfall across NSW varied from 37.71 mm to 147.3 mm, indicating the topographic and climatic influences on extreme rainfall. The outcomes of the study suggested that the future design rainfall will be significantly different from the current BoM estimates for most of the studied stations. The comparison of the results showed that future rainfall in NSW will change from −4.7% to +60% for a 100-year recurrence interval. However, for a 2-year recurrence interval, the potential design rainfall change varies from an approximately 8% increase to a 40% decrease. This study revealed that the currently designed stormwater management infrastructure will be idle in the changing climate.

Evaluation of Five Satellite-Based Precipitation Products for Extreme Rainfall Estimations over the Qinghai-Tibet Plateau

The potential of satellite precipitation products (SPPs) in monitoring and mitigating hydrometeorological disasters caused by extreme rainfall events has been extensively demonstrated. However, there is a lack of comprehensive assessment regarding the performance of SPPs over the Qinghai-Tibet Plateau (QTP). Therefore, this research aimed to evaluate the effectiveness of five SPPs, including CMORPH, IMERG-Final, PERSIANN-CDR, TRMM-3B42V7, and TRMM-3B42RT, in identifying variations in the occurrence and distribution of intense precipitation occurrences across the QTP during the period from 2001 to 2015. To evaluate the effectiveness of the SPPs, a reference dataset was generated by utilizing rainfall measurements collected from 104 rainfall stations distributed across the QTP. Ten standard extreme precipitation indices (SEPIs) were the main focus of the evaluation, which encompassed parameters such as precipitation duration, amount, frequency, and intensity. The findings revealed the following: (1) Geographically, the SPPs exhibited better retrieval capability in the eastern and southern areas over the QTP, while displaying lower detection accuracy in high-altitude and arid areas. Among the five SPPs, IMERG-Final outperformed the others, demonstrating the smallest inversion error and the highest correlation. (2) In terms of capturing annual and seasonal time series, IMERG-Final performs better than other products, followed by TRMM-3B42V7. All products performed better during summer and autumn compared to spring and winter. (3) The statistical analysis revealed that IMERG-Final demonstrates exceptional performance, especially concerning indices related to precipitation amount and precipitation intensity. Moreover, it demonstrates a slight advantage in detecting the daily rainfall occurrences and occurrences of intense precipitation. On the whole, IMERG-Final’s ability to accurately detect extreme precipitation events on annual, seasonal, and daily scales is superior to other products for the QTP. It was also noted that all products overestimate precipitation events to some extent, with TRMM-3B42RT being the most overestimated.

Evaluating the performances of gridded satellite/reanalysis products in representing the rainfall climatology of Ethiopia

This study evaluated performances of the Climate Hazard Group Infrared Precipitation with stations version 2.0 (CHIRPS v2.0) and Multi-Source Weighted-Ensemble Precipitation version 2.8 (MSWEP v2.8) products against observed data. Rainfall climatology was simulated for different agro-ecological zones (AEZs) of Ethiopia during 1991–2020 at different temporal scales. Performance evaluations were made using continuous and statistical performance measures as well as Probability Density Function (PDF). CHIRPS v2.0 for estimating monthly, seasonal, and annual rainfall totals, and MSWEP v2.8 for daily rainfall have shown better performance over all AEZs. The two products display comparable performance for detecting daily rainfall occurrences over alpine AEZ, but MSWEP v2.8 is superior in the rest four AEZs. CHIRPS v2.0 outperforms MSWEP v2.8 for detecting most of the daily rainfall intensity classes over all AEZs. The findings will play a noteworthy role to improve the quality of hydro-climate studies in Ethiopia.

Rainfall extremes on the rise: Observations during 1951–2020 and bias-corrected CMIP6 projections for near- and late 21st century over Indian landmass

In this study, we provide a comprehensive analysis to identify and quantify spatial patterns of heavy, very heavy and extremely heavy rainfall and their trends that have emerged during the last seven decades (1951 to 2020) of monsoon months (June to September) under warming scenario as well as to project these extreme rainfall counts during the near- (2036–2060) and late-21st century (2075–2099) w.r.t. historical period (1990–2014) using bias-corrected Coupled Model Intercomparison Project-6 (CMIP6) multi-model ensemble method. On the basis of daily maximum rainfall occurrences, the Central India, North-East India, Western Ghats and Eastern Ghats are found to be susceptible to extreme rainfall zones over the Indian landmass. The trend distribution during 1951–2020 suggests an increase of 42–63 heavy rainfall events over Orissa, Chattisgarh and parts of Madhya Pradesh and a declination over Uttar Pradesh, Kerala and hilly regions of North-East India. Our study suggests the causal theory for the rise of monsoon rainfall extremes in terms of both dynamics and local-scale thermodynamics over the sub-continent. Moreover, the bias-corrected dataset is developed using Empirical Quantile Mapping (EQM) for historic and projected climate for the three scenarios (SSP1-2.6, SSP2-4.5, SSP5-8.5) using output from 20 General Circulation Models (GCMs) from CMIP6. Hence, the bias-corrected projections suggest that most susceptible places for increasing heavy rainfall extremes likely to be Mumbai, Pune, Panaji in the Western coasts of India (Western Ghats), Itanagar and Shillong in the North-East India, Raipur and Bhopal in the Central India in near- and late-21st century under all scenarios in a warming climate. Thus, the bias-corrected projections from CMIP6-GCMs can be used for hydroclimate impact assessment in Indian region under the changing atmospheric circulation dynamics and warming induced by greenhouse gases.

Improving daily rainfall extremes simulation using the generalized Pareto distribution: a case study in Western Iran

Prediction of the occurrence or non-occurrence of daily rainfall plays a significant role in agricultural planning and water resource management projects. In this study, gamma distribution function (GDF), kernel, and exponential (EXP) distributions were coupled (piecewise) with a generalized Pareto distribution. Thus, the gamma-generalized Pareto (GGP), kernel-generalized Pareto (KGP), and exponential-generalized Pareto (EGP) models were used. The aim of the present study was to introduce new methods to modify the simulated generation of extreme rainfall amounts of rainy seasons based on the preserved spatial correlation. The best approach was identified using the normalized root mean square error (NRMSE) criterion. For this purpose, the 30-yr daily rainfall datasets of 21 synoptic weather stations located in different climates of West Iran were analyzed. The first, second, and third-order Markov chain (MC) models were used to describe rainfall time series frequencies. The best MC model order was detected using the Akaike information criterion and Bayesian information criterion. Based on the best identified MC model order, the best piecewise distribution models, and the Wilks approach, rainfall events were modeled with regard to the spatial correlation among the study stations. The performance of the Wilks approach was verified using the coefficient of determination. The daily rainfall simulation resulted in a good agreement between the observed and the generated rainfall data. Hence, the proposed approach is capable of helping water resource managers in different contexts of agricultural planning.

Generalized linear models for analyzing count data of rainfall occurrences

Having the adequate knowledge about the behavior of climatic variables on the occurrences of rainfall is needed to the country’s economists and agriculturists for saving the country’s people from the devastating natural hazards like flash flood, drought, heavy rainfall, etc. Therefore, the study has been taken initiative to identify the influence of climatic variables for the occurrences of rainfall. The study has been developed generalized linear models (GLMs) for Poisson distribution for weekly and fortnightly count data of daily rainfall occurrences for the summer and monsoon seasons for five regional rainfall stations of Bangladesh. For these models, minimum and maximum temperatures and relative humidity are considered as explanatory variables. For five regional rainfall stations, the model selection procedures AIC and BIC indicate that the GLMs for the Poisson distribution satisfactorily explain the influence of climatic variables for the fortnightly occurrences of rainfall in the summer and monsoon seasons. The GLMs for the summer season of fortnightly occurrences of rainfall indicate that if one unit of relative humidity increases, then the probability of rainy days will be increased by 12 percent in Feni station, 6 percent in Sylhet, Khulna and Rajshahi stations, and 7 percent in Dhaka station. Besides, the GLMs for the monsoon season of fortnightly occurrences of rainfall indicate that if one unit increases of minimum temperature, then the probability of rainy days will be increased by 22 percent, 19 percent, 24 percent, 17 percent and 19 percent in Feni, Sylhet, Khulna, Rajshahi and Dhaka stations, respectively. Further, maximum temperature indicates negative influence on the occurrences of rainfall for all the stations and seasons of the period. The study indicates that the relative humidity for summer season and minimum temperature for monsoon season play remarkable role for changing fortnightly occurrences of rainfall in all the regions of the country.

An Evaluation of Statistical Downscaling Techniques for Simulating Daily Rainfall Occurrences in the Upper Ping River Basin

This study presents an exhaustive evaluation of the performance of three statistical downscaling techniques for generating daily rainfall occurrences at 22 rainfall stations in the upper Ping river basin (UPRB), Thailand. The three downscaling techniques considered are the modified Markov model (MMM), a stochastic model, and two variants of regression models, statistical models, one with single relationship for all days of the year (RegressionYrly) and the other with individual relationships for each of the 366 days (Regression366). A stepwise regression is applied to identify the significant atmospheric (ATM) variables to be used as predictors in the downscaling models. Aggregated wetness state indicators (WIs), representing the recent past wetness state for the previous 30, 90 or 365 days, are also considered as additional potential predictors since they have been effectively used to represent the low-frequency variability in the downscaled sequences. Grouping of ATM and all possible combinations of WI is used to form eight predictor sets comprising ATM, ATM-WI30, ATM-WI90, ATM-WI365, ATM-WI30&90, ATM-WI30&365, ATM-WI90&365 and ATM-WI30&90&365. These eight predictor sets were used to run the three downscaling techniques to create 24 combination cases. These cases were first applied at each station individually (single site simulation) and thereafter collectively at all sites (multisite simulations) following multisite downscaling models leading to 48 combination cases in total that were run and evaluated. The downscaling models were calibrated using atmospheric variables from the National Centers for Environmental Prediction (NCEP) reanalysis database and validated using representative General Circulation Models (GCM) data. Identification of meaningful predictors to be used in downscaling, calibration and setting up of downscaling models, running all 48 possible predictor combinations and a thorough evaluation of results required considerable efforts and knowledge of the research area. The validation results show that the use of WIs remarkably improves the accuracy of downscaling models in terms of simulation of standard deviations of annual, monthly and seasonal wet days. By comparing the overall performance of the three downscaling techniques keeping common sets of predictors, MMM provides the best results of the simulated wet and dry spells as well as the standard deviation of monthly, seasonal and annual wet days. These findings are consistent across both single site and multisite simulations. Overall, the MMM multisite model with ATM and wetness indicators provides the best results. Upon evaluating the combinations of ATM and sets of wetness indicators, ATM-WI30&90 and ATM-WI30&365 were found to perform well during calibration in reproducing the overall rainfall occurrence statistics while ATM-WI30&365 was found to significantly improve the accuracy of monthly wet spells over the region. However, these models perform poorly during validation at annual time scale. The use of multi-dimension bias correction approaches is recommended for future research.

Investigating teleconnection patterns associated with the rainy season of the northern northeast Brazil using a hidden Markov model

The interannual variability of the northern northeast Brazil (NNB) rainfall is directly affected by the dynamics of large-scale systems through atmospheric circulation. In this context, a hidden Markov model (HMM) was used to describe the daily rainfall occurrence and intensity at four meteorological stations of the Metropolitan Region of Fortaleza (MRF) in the NNB, and the global teleconnection patterns that influence precipitation regimes during the rainy season (February, March, April and May) from 1975 to 2013. An HMM with 4 states was set up and interpreted as: very rainy (1), rainy (2), less rainy (3), and dry (4) weather conditions. They agree satisfactorily with the interannual variability of the rainy season in this region. State 2 is the only one which showed a statistical trend, indicating a probable decrease of precipitation occurrence in the rainy season. Results also show that the meteorological weather associated with both states 2 and 4 is strongly related to the El Nino-Southern Oscillation (ENSO), the North Atlantic tripole and are intrinsically conditioned to the large-scale atmospheric teleconnections of the Northern Hemisphere. All those mechanisms modulate the shift of the Intertropical Convergence Zone (ITCZ) southward (state 2) or northward (state 4), thus affecting the precipitation occurrence over the NNB. State 1 is distinguished by the influence of the Atlantic Meridional Mode (AMM) and the ITCZ displacement further south, while state 3 is identified by the absence of teleconnection patterns.

Non-homogeneous hidden Markov model for downscaling of short rains occurrence in Kenya

Non-homogeneous hidden Markov model (NHMM) is applied in modeling of daily rainfall occurrences across 16 synoptic stations in Kenya. The time series of the data sets was during the October–December (OND “short rains”) season from 1979 to 2005. The tool assumes that the diurnal rainfall events at a network of observing stations are influenced by unobserved states, that is, “weather states.” These states’ evolution is modeled based on a first-order Markov criterion with state-to-state transition probabilities conditioned on some atmospheric variable indices. The five states are selected using the Bayes information criterion (BIC). To downscale daily rainfall occurrences across 16 stations, a NHMM employed global circulation model (GCM) projection outputs for daily precipitation and sea surface temperatures during the study period. The interannual variability of the mean GCM simulated precipitation and mean historical stations rainfall depicts a weak correlation though significant at 90% confidence level. Thus, it implies that GCM-NHMM simulations do not simulate the rainfall occurrences well. The consecutive wet spell length between the historical rainfall datasets and GCM-NHMM simulated precipitation for 90-day frequencies shows a strong positive correlation significant at 95% confidence level. The findings from this study reveal that the modeling tool is suitable for statistical downscaling of daily rainfall occurrences at multisite stations network. The statistical inference from the model is applicable for drought/flood preparedness, water resource management, and inputs into crop models.

Statistical tool for modeling of a daily precipitation process in the context of climate change

Abstract The present study proposes a climate change assessment tool based on a statistical downscaling (SD) approach for describing the linkage between large-scale climate predictors and observed daily rainfall characteristics at a local site. The proposed SD of the daily rainfall process (SDRain) model is based on a combination of a logistic regression model for representing the daily rainfall occurrences and a nonlinear regression model for describing the daily precipitation amounts. A scaling factor (SR) and correction coefficient (CR) are suggested to improve the accuracy of the SDRain model in representing the variance of the observed daily precipitation amounts in each month without affecting the monthly mean precipitation. SDRain facilitates the construction of daily precipitation models for the current and future climate conditions. The tool is tested using the National Center for Environmental Prediction re-analysis data and the observed daily precipitation data available for the 1961–2001 period at two study sites located in two completely different climatic regions: the Seoul station in subtropical-climate Korea and the Dorval Airport station in cold-climate Canada. Results of this illustrative application have indicated that the proposed functions (e.g. logistic regression, SR, and CR) contribute marked improvement in describing daily precipitation amounts and occurrences. Furthermore, the comparison analyses show that the proposed SD method could provide more accurate results than those given by the currently popular SDSM method.

Establishing a daily rainfall occurrence simulation model for the Langat River catchment, Malaysia

For the study of water resources of a catchment, an immediate task would be to establish a good model for predicting the probable daily rainfall occurrence and rainfall amount. This study presents the simulation of daily rainfall occurrence using the generalized linear model (GLM), the non-homogeneous hidden Markov model (NHMM) and the bootstrap aggregated classification tree (BACT) model. The major challenge of NHMM is the determination of optimum number of hidden states, which can be achieved using the Bayesian information criterion score. While the determination of number of grown tree is another challenge for BACT model, this critical task can be achieved with the help of out-of-bag classification error. Both the NHMM and BACT model outperformed the GLM to capture the rainfall persistence and spell lengths distribution. Through the validation phase, the BACT model exhibited better performance with the higher indices of probability of detection, critical success index, Heidke skill score and Peirce skill score, than other models. The prediction ability of the NHMM is equivalent to an unskilled random forecast with the skill scores nearly equal to zero. At the end, the BACT model was recommended as the appropriate daily rainfall occurrence model for this study.

Monitoring the Underlying Probability of Daily Rainfall Occurrence in West Java over Space and Time by Means: A Bayesian Spatiotemporal Model Approach

Monitoring the underlying probability of daily rainfall occurrence is needed for many applications, such as in agriculture, hydrology and ecology, epidemiology, maritime and tourism and society in general. We use Climate Hazard InfraRed Precipitation with Station Data (CHIRPS) to obtain the estimated probability of daily rainfall occurrence. The model has been used based on Kitagawa (1987). We used the Kitagawa model with introducing the spatial and spatiotemporal dependencies in the Binomial smoothing model using Bayesian spatiotemporal model approach by means of the Integrated Nested Laplace Approach (INLA) and applied this model for estimating the underlying probability of daily rainfall occurrence in West Java, Indonesia. Eight different model were tested and model 8 was found as the best model based on Bayesian and classical criterions. We found the circular temporal trend of random walk order one and spatiotemporal interaction type IV are the two most important components in explaining the change of probability of daily rainfall occurrence. The daily precipitation chances reached 90% from November up to February for every year.

Modeling of Daily Rainfall Extremes, Using a Semi-Parametric Pareto Tail Approach

Various approaches have been widely proposed for simulation of the occurrence and the amount of daily rainfall. In this study, a piecewise distribution approach has been developed to improve extreme event amount simulation. The gamma-generalized Pareto (GGP) approach employs a combination of the generalized Pareto (GP) and the gamma density estimation method to model the daily rainfall distribution. Furthermore, three stochastic rainfall time series generations have been developed and compared to simulate the daily rainfall occurrence based on the first-order Markov chain (MC1), the second-order Markov chain (MC2) and the third-order Markov chain (MC3) approaches. 30 years daily datasets from 5 synoptic stations have been used in the semi-arid extra cold in Iran. The performance of different approaches has been compared using Akaike information climate criterion (AIC) and root mean square error (RMSE). Results show that MC1 performs relatively better than MC2 and MC3 for daily rainfall occurrence modeling. Results also show that the GGP probability density performs better to reproduce extreme daily rainfall compared with gamma, GP and exponential distributions.

Pronóstico de la ocurrencia de precipitación diaria en un gradiente altitudinal en el Sur del Ecuador mediante un generador climático

El pronóstico de precipitación es fundamental para mejorar la gestión de los recursos hídricos tanto para proyectos de aprovechamiento como de reducción de riesgos. Debido a su alta variabilidad, es un reto realizar un buen pronóstico de lluvia. En el presente estudio se empleó un generador climático (GC) para investigar la calidad del pronóstico de ocurrencia de precipitación diaria en una zona de montaña. El GC implementado usó como predictores a tres variables: la variable binaria ocurrencia del día anterior (Kt-1), las temperaturas máximas y mínimas del día anterior (Txt-1, Tnt-1, respectivamente); y dos covariables: las anomalías de la Temperatura mensual Superficial del Mar de las Regiones 1+2 y 3.4 de El Niño-Oscilación del Sur (Niño 1+2 y Niño 3.4 respectivamente). Determinamos que las variables Kt-1, Tnt-1 y la covariable Niño 3,4 mejoran el ajuste en el pronóstico. Encontramos diferencias notables en el número de días consecutivos secos y lluviosos en el gradiente altitudinal en un periodo lluvioso. El estudio permitió el planteamiento de varias hipótesis a partir del uso del GC las cuales ayudan a la comprensión del funcionamiento del sistema climático y el mejoramiento del pronóstico de precipitación.

Projections of future rainfall for the upper Ping River Basin using regression-based downscaling

The objective of this study was to use regression modelling, a form of statistical downscaling technique, to predict the daily rainfall occurrence and rainfall amounts for a small river basin, the upper Ping River Basin (UPRB) in northern Thailand. Daily historic (1960–2005) rainfall and a number of daily reanalysis variables (NCEP/NCAR) were used to create regression models that estimate the probabilities of rainfall occurrence (wet days) and amounts (rainfall depth) at each of 29 rain gauge stations located in and around the UPRB. The regression models were calibrated using historic (1960–1989) data and validated using historic (1990–2005) data. Regression models were later applied to historic (1960–2005) GCM outputs (MPI-ESM-LR model) which were adjusted to correspond to the selected reanalysis variables using the Nested Bias Correction (NBC) technique. Rainfall occurrence and amounts were predicted for the periods 2006–2050 and 2051–2100 for RCP2.6, RCP4.5, RCP8.5 scenarios. Results show that the effects of climate change vary considerably across the catchment, with significantly declines in both the number of wet days and rainfall depth in the wet- and especially the dry-season in the middle of the catchment but obviously increase slightly towards the northern part of the catchment. Since the stepwise regression was used to select the atmospheric variables to form the regression models for simulating rainfall occurrence and amount, different stations have their own predictors and can influence future rainfall to vary significantly between 29 rain gauge stations. If the top three predictors were selected to form the regression models for simulating rainfall occurrence and amount for all stations, the future rainfall characteristics possibly change and can be used to compare with those of presented in this study. It will show either atmospheric predictors or climate change scenarios would have more effect on future rainfall characteristics.

Analysis of the stochastic model of the Markov chain on daily rainfall occurrence in the state of Santa Catarina, Brazil

PurposeThe purpose of this paper is to evaluate the seasonal and spatial variations in the statistical descriptors of the Markov chain model as well as the expected values of the length of dry and wet days and to estimate the probability of dry and rainy sequences in the state of Santa Catarina.Design/methodology/approachDaily rainfall data from 1970 to 2013 of five rainfall stations in the state of Santa Catarina were used. To model the sequence of dry and wet days, the first order of the Markov chain was used. The statistical descriptors of the Markov model were evaluated, as well as the expected values of the length of dry and wet days and the number of dry and rainy days for each month. Along with geometric distribution, the probability of occurrence of sequences of dry and rainy days was determined. The adherence of the data to geometric distribution was evaluated using the Kolmogorov-Smirnov test.FindingsThe results showed that there is a seasonal and spatial variation in Markov model descriptors and also in the duration of the dry and rainy periods. These variations may be related to the mechanisms responsible for the formation and distribution of rainfall in the state, such as the air masses and relief. The Lages station, located in the Plateau of Santa Catarina, had the highest P00 values, reflecting more stable conditions of the atmosphere. In autumn and winter, no marked differences were found between the coastal stations and west of the state. The geometric distribution was adequate for estimating the probability of dry and rainy days.Originality/valueAlthough some work has already been carried out on the modeling of the Markov chain in the state of Santa Catarina, this study was found to be more complete with the use of various statistical descriptors of the model and its application in estimating the duration of the cycles of dry and wet periods and the number of rainy days in the period.

Variations in the sequences of daily rainfall across Nigeria

The study compared the sequences of daily rainfall over coastal southern and semi-arid northern Nigeria. Daily rainfall occurrences for 41 years (1971–2011) over four meteorological stations in Lagos, Rivers, Borno, and Katsina were analyzed using frequency analysis and Markov chain model. Findings indicate that the coastal area had a predominance of 2–4-day wet spells while the semi-arid area showed a wet spell distribution that is geometric in nature with 1-day spell predominance. The dry spell behavior was nearly the opposite of the wet spell occurrence. The coastal region showed a dry spell of 1–4-day spell predominance while the semi-arid region showed a predominance of higher dry spells of 2–6 days. Accumulation of the amount of rainfall in each spell also showed that much rainfall from the coastal area was obtained from rains of spells of 3 days and above while the semi-arid had more of its rain from spells of 1–3 days. The mean annual rainfall was 1423.75 mm (Lagos), 2173.56 mm (Rivers), 517.50 mm (Katsina), and 578.34 mm (Borno). The wettest month was June (274.08 mm) in Lagos, September (378.18 mm) in Rivers, and August in Katsina and Borno (172.98 and 184.81 mm, respectively). The driest months were January for Lagos and Rivers (15.77 and 18.96 mm, respectively) and November–February for Katsina and Borno (0–0.06 mm). This showed that the coastal areas had nearly three times the volume of rain in the semi-arid area. The study further showed that onset of rain for the coastal area was March/April while the cessation of rainy season was October/November. On the other hand, the onset of rainy season in the semi-arid area was May/June and cessation of rainy season was September. Findings portend drier days for the semi-arid area due to dry spell persistence and hence, the consequent challenges of providing artificial water supply for agriculture and other purposes especially from October to May.

Markov Chain Decomposition of Monthly Rainfall into Daily Rainfall: Evaluation of Climate Change Impact

This study evaluates the effect of climate change on daily rainfall, especially on the mean number of wet days and the mean rainfall intensity. Assuming that the mechanism of daily rainfall occurrences follows the first-order Markov chain model, the possible changes in the transition probabilities are estimated by considering the climate change scenarios. Also, the change of the stationary probabilities of wet and dry day occurrences and finally the change in the number of wet days are derived for the comparison of current (1x CO2) and 2x CO2conditions. As a result of this study, the increase or decrease in the mean number of wet days was found to be not enough to explain all of the change in monthly rainfall amounts, so rainfall intensity should also be modified. The application to the Seoul weather station in Korea shows that about 30% of the total change in monthly rainfall amount can be explained by the change in the number of wet days and the remaining 70% by the change in the rainfall intensity. That is, as an effect of climate change, the increase in the rainfall intensity could be more significant than the increase in the wet days and, thus, the risk of flood will be much highly increased.