Simulation of Rainfall Occurrence in Qazvin Synoptic Station Using Probability Models

Simulation of Rainfall Occurrence in Qazvin Synoptic Station Using Probability Models

Ababaei B.?
Ph.D. Candidate in Agriculture Engineering (Irrigation and Drainage), Dep. of Irrigation and Reclamation, Faculty of Agricultural Engineering and Technology, University of Tehran
Sohrabi T.M.
Prof., Dep. of Irrigation and Reclamation, in Faculty of Agricultural Engineering and Technology,University of Tehran
Mirzaei F.
Assistant Prof., Dep. of Irrigation and Reclamation, Faculty of Agricultural Engineering and Technology, University of Tehran

Extended Abstract

Introduction
Models of observed daily weather sequences are frequently used in water engineering design, and agricultural, ecosystem or climate change simulations because observed ground-based meteorological data are often inadequate in terms of their length, completeness or spatial coverage. These statistical models are also known as ‘weather generators’ since they can fill missing data or produce indefinitely long synthetic weather series by simulating key properties of observed meteorological records (i.e., daily means, variances and co-variances, frequencies, extremes, etc.). To date, the majority of weather generators have focused on the precipitation process in recognition of the dominant control exerted by rainfall on many environmental processes, and due to the complexity of building internally consistent, multivariable models (Hutchinson, 1995). However, companion algorithms that simulate other meteorological variables are also in routine use.
Rather than simulating rainfall occurrences day by day, spell-length models operate by fitting probability distributions to observed relative frequencies of wet and dry-spell lengths. This kind of model is sometimes called an ‘alternating renewal process’ (Buishand, 1977; 1978; Roldan and Woolhiser, 1982), in that random numbers are generated alternately from the wet and dry spelllength distributions. That is, a new spell length (L) is generated only when a run of consecutive wet or dry days has come to an end, at which point a new spell of the opposite type is simulated.

Methodology
In this research, the performance of different probability models were analyzed for simulating the distribution of dry and wet spells in Qazvin synoptic station (period 1959-2008), using four methods:
1) Fitting the best models to the data of each month;
2) Fitting geometric distribution to the data of each month;
3) Fitting the best models to the data of each 3-month periods;
4) Fitting the best models to the data of each season.

The models were:
1) Geometric Distribution (GD);
2) Log Series Distribution (LSD);
3) Mixed Two Geometric Distribution (MGD);
4) Mixed Geometric Poisson Distribution (MGPD);
5) Mixed Geometric Truncated Poisson Distribution (MGTPD);
6) Mixed Two Log Series Distribution (MLSD);
7) Mixed Log Series Geometric Distribution (MLGD);
8) Mixed Log Series Poisson Distribution (MLPD);
9) Mixed Log Series Truncated Poisson Distribution (MLTPD);
10) Negative Binomial Distribution (NBINO);
11) Poisson Distribution (PD).

Results and Discussion
The results showed that in simulating dry spells, 3-parameter models (specially the mixture of two geometric distributions and the mixture of a geometric and a Poisson distribution) were selected as the best models. These revealed better performance of these models in simulating longer periods because in simulating wet spells series (which includes shorter periods), 1-parameter models were selected as the best models. For wet spells, the bias (RMSE and MAE) of all methods increased in the dry periods of the year. This statement holds also for dry spells because the biases increase with the start of the wet periods of the year. Again, in simulating dry spells, the performance of the first and the second methods were better in keeping the statistics of observed series. But in simulating wet spells, the third and the fourth methods performed better. The first method performed better in simulating the transitional probabilities from a dry day and the third method outperformed the other methods in simulating the transitional probabilities from a wet day.
Conclusion
The results revealed that the 3-parameter models outperformed the 1- and 2-parameter models in simulating long spells. So, it could be recommended to use such models in order to simulate (long) dry spells. Also, it was concluded that choosing the best models (according to AIC criteria) for each month and using the geometric distribution for all months could results in a better simulation of the statistics of the observed series. But, aggregating the monthly data into 3-month and seasonal periods could increase the accuracy in the simulation of the wet spells. It is recommended to analyze the performance of these probability models in other climatic stations in order to choose the best model for each station.

Keywords: Rainfall Occurrence, Probability Models, Dry Spells, Wet Spells, Qazvin Synoptic Station.