واسنجي منطقه‌اي ضرايب تجربي حاكم بر نمايه شدت خشكسالي پالمر

Calibration of internal empirical coefficients in the Palmer Drought Severity Index

يكي از شناخته شده‌ترين نمايه هاي خشكسالي، نمايه شدت خشكسالي پالمر مي‌باشد كه به صورت بسيار گسترده مورد استفاده قرار گرفته است. هدف از اين تحقيق استخراج و واسنجي ضرايب تجربي موسوم به "عوامل استمرار" در نمايه شدت خشكسالي پالمر مي‌باشد كه همواره عاملي محدود كننده در استفاده از اين نمايه بوده اند. در اين تحقيق، نمايه توزيعي شدت خشكسالي پالمر با استفاده از داده هاي شبكه‌اي شده خاك و هواشناسي با تفكيك مكاني 4 كيلومتر توسط نرم افزار MATLAB در مقياس كشوري محاسبه و استخراج شد. سپس توزيع مكاني مقادير عوامل استمرار در دو حالت خشك و تر استخراج شد و ميانه اين مقادير با مقادير پيشنهادي پالمر براي اين عوامل مقايسه گرديد. نتايج نشان مي‌دهد كه در مقايسه با ضرايب پيشنهادي پالمر (897/0 p= و 33/0q=)، مقادير واسنجي شده p و q بترتيب از  0 تا 1/1 و از 0 تا 5/3 متغير است. بررسي ميانه مقادير بدست آمده براي عوامل استمرار نشان مي دهد كه در مقايسه با منطقه مورد مطالعه پالمر، مقدار نمايه خشكسالي در هر دوره به تغييرات بارندگي بيشتر از مقدار نمايه در دوره هاي قبل حساس است. بنابراين نميتوان مستقيما از ضرايب تجربي پيشنهادي پالمر در ساير مناطق بدون واسنجي استفاده نمود.

Introduction Drought refers to the shortterm or longterm period’s association with the lack of rainfall, increased temperature and reduced humidity. Perhaps one of the most widely recognized drought indexes is Palmer Drought Severity Index (PDSI) presented by Palmer in 1965 to quantify the intensity of drought. Since then, numerous researches have been conducted based on this index and some attempted to modify the index. The general aim of this study was to derive and calibrate the empirical coefficients named as duration factors in the Palmer drought severity index by the method introduced by Wells et al (2004) in a country scale.   Materials and Methods Study area The study area located between latitude of 25 to 40 degree in North and longitude of 44 to 64 degrees in East. Average annual rainfall is estimated as 240 mm per year.   Palmer moisture model PDSI is based on a lumped soil moisture model with specific supply and demand. Supply of moisture from precipitation is absorbed into the soil. Excess moisture or lack of moisture (d) is essentially determined in a month and is calculated using the following equation:  (1)                                             Where P is rainfall and   is rainfall called as CAFEC (suitable for the climatic conditions). P is calculated as follows:                                                           (2) Where, subscript i refer to a year. Moisture diversion (Z) simply obtains by multiplying d in climatic parameter (K):                                                                                                        (3) In procedure of Palmers index three intermediate indices are introduced as follows: X1 is wet period, X2 extremely dry periods, and X3 of the duration factor in the recent period. The actual amount of PDSI is determined by selecting one of the three indices according to a set of rules. For instance, X3 is calculated as:                                                                                                       (7) Values ​​of p and q which are the subjects of this study are considered as 0.897 and 0.3 respectively. P and q are empirical constants and recognized as duration factor. These parameters were acquired using two climatic data sets in the studies conducted by Palmer in 1965. To conduct the study, the temperature and precipitation data from 296 synoptic stations and over 1,500 rain gauge stations for the period beginning in 1975 and early 2011 were collected. Then, temperature data was converted to the raster format using a multivariate correlation technique (latitude and longitude and altitude digitization). Rainfall data was also spatially distributed using an IDW interpolation method for each month of each year for the period of 1975 to 2011 at a national scale. Palmer model was performed on a distributed raster scheme with 4 kilometer spatial resolution.   Results In Figures 1 and 2, spatial distribution of duration factors q and p is shown in the dry and wet cases respectively. As you can see, the coefficients show different spatial variations in wet and dry conditions and the maps can be used to extract the Palmer Index in any region. For a more detailed study, relative frequency curves of  duration factors  p and q are derived for the both wet and dry periods. The results indicate that value of p in the dry period is more in comparison to its value in the wet period and for q the situation is reversed. This means that in drought period, the index at each step, rather than changes in precipitation and soil moisture is sensitive to the value of the index on the previous step, while in wet period, the situation is reversed. This means that the climate of the study area (all areas) typically has a tendency to dryness.   Conclusion The regional empirical coefficients of the Palmer Drought Severity Index in the last 36 years, indicating the need for calibration of Palmer (SCPDSI) in most parts of Iran. As general, the climate of the study area (all areas) typically has a tendency to dryness.