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Innovative Polygon Trend Analysis (IPTA) and applications
Journal of Hydrology 575 (2019) 202–210
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Research papers
Innovative Polygon Trend Analysis (IPTA) and applications Zekâi Şen a b
a,b
a,b,⁎
, Eyüp Şişman
a,b
, Ismail Dabanli
T
Istanbul Medipol University, School of Engineering and Natural Sciences, Civil Engineering Department, Kavacık, 34181 Istanbul, Turkey Istanbul Medipol University, Climate Change Researches Application and Research Center, (IKLIMER) Kavacık, 34181 Istanbul, Turkey
ARTICLE INFO
ABSTRACT
This manuscript was handled by Huaming Guo, Editor-in-Chief, with the assistance of Philippe Negrel, Associate Editor
Trend analysis is continuously in the research and application agenda due to climate change effect searches on various engineering, social, economic, agriculture, environmental and water resources design, management, operation and management studies. Classical trend analysis is useable for holistic trend identification and then statistical quantification as for its intercept and slope. The main drawbacks in these classical approaches are the set of fundamental assumptions such as the serial independence of the given time series, pre-whitening, normality of the data and non-existence of serial comparison among different sections of the same record. This paper explains a non-parametric approach to avoid almost all these difficulties by simple methodology, which is referred as the Innovative Polygonal Trend Analysis (IPTA). Such an approach helps not only to identify the trend in a given series, but also trend transitions between successive sections of the two equal segments from the original hydro-meteorological time series leading to trend polygon, which provides a productive basis for finer interpretation with linguistic and numerical interpretations and inferences from a given time series. The application of the IPTA is presented for rainfall records from New Jersey, USA, Danube River and Göksu River discharge records from Romania and Turkey.
Keywords: Hydro-meteorology IPTA Polygon trend Stochastic Time series Trend analysis Trend slope
1. Introduction Hydro-meteorological variable average changes and variabilities in the standard deviation are very essential in different human activities such as water supply, groundwater recharge, hydro-electric energy generation, agricultural activities and irrigation applications. It is expected that recent global warming and consequent climate change impacts may accelerate these changes, and therefore, their control should be done according to objective methodologies. In the literature, there are various methodologies for the assessment of time series trend component and variability changes (Mann, 1945; Sen, 1968; Kendall, 1975; Şen, 2012). A common definition of a trend can be generally directional and in the forms of steadily increasing or decreasing average tendency in a time series. It is possible to recognize such tendencies in a given time series visually. However, their objective identification by scientific and methodological approaches have rather restrictive assumptions. Two implicit features of any trend are its relatively slow average change along time axis and smoothness that it is a continuous straight-line. There may be also non-linear (stochastic) trend components in a hydro-meteorological time series. The purpose of trend analysis is to make future predictions on the objective, quantitative and systematic detection, identification and prediction mechanisms
whereas stochastic component shows itself as the residual around the trend. Such mechanisms are available mostly through the statistical procedures with a set of restrictive basic assumptions. Trend detection analysis has a special place in any statistical analysis of hydro-meteorological, economy, geophysics, quality control, and similar time series studies. Predominantly temporal trends are the main concern, but in some topics especially in geology and engineering works, spatial trend searches are significant for regional assessments. For instance, Trend Surface Analysis (TSA) has been applied by geologists for more than 60 years to separate an observed contour map into two components: a regional trend and a local fluctuation component (Davis, 2002). This approach is limited by using a global polynomial method in trend modeling. It does not allow geologist’s input to achieve an optimal removal of undesirable trend. This leads to a low resolution and sometimes artifacts in highlighting interested features. Climate change and global warming have led to a dramatic increase in trend analysis application of hydro-meteorological time series as temperatures, humidity, precipitation, evaporation, stream flow. The number of trend researches has been increased since the pioneering works of Mann (1945) and Kendall (1975), the couple of which is referred classically as the Mann-Kendal (MK) trend test. This method has been applied frequently by many researches (Burn, 1994; Bocheva
⁎ Corresponding author at: Istanbul Medipol University, School of Engineering and Natural Sciences, Civil Engineering Department, Kavacık, 34181 Istanbul, Turkey. E-mail address: [email protected] (E. Şişman).
https://doi.org/10.1016/j.jhydrol.2019.05.028 Received 8 November 2018; Received in revised form 12 April 2019; Accepted 8 May 2019 Available online 10 May 2019 0022-1694/ © 2019 Elsevier B.V. All rights reserved.
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Recent (2nd) half sub-series
et al., 2009; Kyselý, 2009; Korhonen and Kuusisto, 2010; Reihan et al., 2012; Wilson et al., 2010; Jones et al., 2015; Güçlü, 2018; Zhang et al., 2015; Yu et al., 1993). Besides this, Theil (2011) and Sen (1968) investigated Theil-Sen approach for supporting the MK test helps to detect the magnitude of the trend. Applications of this methodology can be seen in papers by Sayemuzzaman and Jha (2014); Swain et al. (2015) and Bari et al. (2016). Şen (2012) proposed Innovative Trend Analysis (ITA) method, which provides trend identification from inductive and deductive perspectives. This innovative non-parametric approach and its severalversions are analyzed by many researches (Dabanli and Şen, 2018; Şen, 2014, 2017; Alashan, 2018a,b; Güçlü et al., 2018a,b; Dabanlı et al., 2016; Sonali and Nagesh Kumar, 2013; Tabari et al., 2017; Wu and Qian, 2017; Elouissi et al., 2016; Mohorji et al., 2017; Almazroui et al., 2018). Trend detection in holistic manner by aforementioned parametric and non-parametric methods is important, but they do not reflect periodical, say monthly, trend features, which is very essential for depiction of seasonal trend behaviors. Especially, seasonal trend detection can help to regulate or manage water resources systems, agriculture and irrigation works. Therefore, new approach is suggested by evolving ITA procedure to fulfill this gap in trend analysis. The goals of this paper are to explain procedures of IPTA templates and to present its applications for discussions. Such a trend approach provides physical aspects of average and standard deviation seasonal variations that are essential and refined parts hidden in holistic annual trend behaviors. The templates that show transitional trend components between successive months are presented for different hydrometeorological records in Turkey, Romania and United States.
May
Dec Old (1st) half sub-series Fig. 1. A hypothetical Innovative Polygon Trend Analysis (IPTA) template for monthly records.
It is possible to consider this matrix in two halves as the upper (the first) and lower (the second) parts by consideration of the indicator i as i = 1, 2, …, n/2, and i = n/2 + 1, n/2 + 2, … n, respectively. Subsequently, one can calculate the monthly averages and the standard deviations from each half matrix columns as upper half ( x u,2 , x u,2 , , x u,12) , and lower half ( xl,2 , xl,2 , , xl,12 ) and likewise the standard deviations as (su,1, su,2 ,su,12) , and (sl,1, sl,2 ,sl,12 ) , respectively. In the same way it is possible to identify the maximum and minimum values for the upper and lower parts as (M1, M2, , M12), and (m1, m , , m12 ), respectively. Provided that these parameters are considered in two sets then the IPTA version of the ITA template appears as in Fig. 1, where each month is shown as the vertex of the polygon. Successive monthly points are connected by straight-lines, which indicate the transition from one month to the next one. A straight-line provides a set of qualitative and quantitative trend information. The scatter of monthly values in this graph is dependent on the effects of different hydro-meteorological phenomena such as storm types, frequency and magnitude, weather patterns, morphology, human settlement, vegetation, land use and land change. In a regular polygon, there is generally a rising limb followed by a falling sequence. For instance, in the Fig. 1 starting from January (Jan) through points February (Feb), March (Mar), April (Apr), May (May), up to June (Jun), the monthly values are in rise. On the other hand, starting from June (Jun) through July (Jul), August (Aug), September (Sep), October (Oct), November (Nov), December (Dec), and ending in January (Jan), a falling sequence exists. The comparative difference between the rising and recession limbs also provides how the internal change in the concerned hydro-meteorological variable changes. For instance, during the rising sequence, there are more frequent and abundant rainfall occurrences, whereas along the falling sequence opposite situations take place. Although the template in this figure provides rather systematic polygons with one loop, however depending on the physical circumstances, there may be two or even more complex loops. Physically, the more dynamic and chaotic a hydro-meteorological event, the more complex polygon are tending to appear. However, in the case of regular
2. Methodology It is by now well-known that the ITA as suggested by Şen (2012, 2014, 2017a,b) provides visual interpretations and numerical quantifications of a given hydro-meteorological data set classification into “Low”, “Medium” and “High” groups. If necessary one can apply the same technique for two, three or more sub-series of equal length from the mother time series. In the application of ITA, there is no restrictive assumption, which first provides subjective visual interpretations leading to objective linguistic inferences. The slope and intercept of the monotonic trend can be calculated numerically, and finally, the significance test can be applied (Şen, 2017a). IPTA can be applied on several time scales (i.e. daily, monthly, annual…etc). In case of monthly statistical parameters, basically arithmetic average and standard deviation are taken as template construction between 12 set of each parameter from the first half of the mother time series versus to the second part 12 monthly values. These twelve values can also be adapted for any other monthly value such as the skewness coefficient, maximum or minimum, which provide further detailed information about the monthly variations within the data. Although in this paper monthly records are considered, it is possible to expand such a procedure to weekly or even daily data treatment in the same manner. Let us consider a monthly hydro-meteorological time series as x1, x2, …, xn, where n is the number years. This sequence can be arranged into a monthly matrix as,
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phenomenon, the polygons end up with a single loop. For instance, rainfall events might have comparatively more polygonal loops than runoff, because after all the runoff discharges are rather dampened loops due to the collective behavior of a drainage area. In the scatter diagram for monthly records, the straight-lines appear as a 12-vertice polygon with different side lengths and slopes. In general, simply a straight-line expression can be obtained after knowing the coordinates of each successive scatter points on the IPTA template; hence each trend line slope can be calculated. Holistically, IPTA template appears in the form of 12-sided non-linearity within the monthly hydro-meteorological time series. Furthermore, a IPTA template for monthly records provides a basis for qualitative and quantitative interpretations and calculations about the hydro-meteorological system leading to the following useful information:
and upper limits of expected hydro-meteorological variable monthly amounts variation domain. Similarly, any vertical line depicts the lower and upper limits as well as the range of hydrometeorological amount, (h) The smaller the area of the polygon, the more consistent the monthly precipitation and the more stable the hydro-meteorological event occurrence, (i) The smaller the overall slope of the polygon from the horizontal axis, the more intensive the hydro-meteorological event occurrence, (j) In any water resources project planning, operation, maintenance and development the IPTA template provides values for an effective and systematic assessment. These general characteristics of the polygon diagrams reflect many quantitative and qualitative properties of the hydro-meteorological phenomena.
(a) The straight-line between two consecutive months indicates the change in the monthly values. The closed polygon implies the natural balance behavior of the hydro-meteorological variable concerned for one year, (b) The consecutive monthly changes are represented by the length of each straight-line length, (c) If the slope of each straight-line in the IPTA template is close enough to each other both in vertical and horizontal direction, it implies that the relative monthly rates contribute insignificantly to the mean of hydro-meteorological variation for each consecutive month. Likewise, all the straight-lines in the IPTA template first provide explanation on annual basis 12-month variation for qualitative (linguistic) inference at each record location, (d) Each polygon side implies the assumption that there is a linear change between consecutive months. The linearity assumption smaller than one-year implies more realistic results in the trend analysis, (e) If the slopes of all the straight-lines in an IPTA template are not different from each other, all of the sides appear around a single global direction then connection of the polygon vertices provide a broken line, which is very close to the global regression line fit. In this case, the polygon is very narrow, which means that the internal change within the hydro-meteorological variable is quite homogenous, isotropic and has uniform variation behavior, whereas comparatively wider polygons indicate heterogeneous temporal variation, (f) In general, any polygon with a rising form implies that the prevailing conditions are almost in balance. On the contrary, there may arise two or more polygons (loops) rather than a single one as indicated in Fig. 2. (g) Any horizontal line intersection with the polygon provides lower
3. Application The application of the IPTA concept principles is given for three hydro-meteorological monthly records from different parts of the world. These are the New Jersey (USA), where very long precipitation records are available from 1895 up to 2010, Danube River (Romania) monthly flows from 1882 up to 2000 and runoff records from Göksu River (Turkey) from 1936 up to 2000. The locations of each region are presented in Figs. 3a, 3b and 3c. In all the IPTAPTA template graphs in Figs. 4–7 are related to various New Jersey monthly precipitation records. There are significant differences as for the statewide, coastal, northern and southern regions. Table 1 presents numerical values of mean and standard deviation for coastal regions for the first and second halves sub-series in addition to the trend lengths and slopes. For instance, in arithmetic mean figure, individually five of the months (January, February, June, July and August remain below the 1:1 (45°) no trend straight-line, which implies that there were less rainfall monthly averages during the recent half (1953–2010) than the first half (1985–1952). However, in other months, the opposite situation is valid, i.e. there are rainfall increments. Especially, September, October, November, December, April and March periods have rather very complicated and inconsistent rainfall behaviors. Similarly, in standard deviation IPTA graph July, August and September appear under the 1:1 line, indicating that there are tendencies towards decreasing trends, whereas increasing trends are valid in other months. The following points are significant in the interpretation of the monthly arithmetic averages and standard deviation scatters and tables.
Recent (2nd) half sub-series
1) Since there is no regular and stable appearance of successive monthly points as it is usually expected like the polygon in Fig. 1. The mean monthly precipitation and standard deviation at the coastal region of New Jersey state are not stable, because there are non-systematic shifts from month to month, 2) The precipitation phenomenon in this region does not reflect homogeneous and isotropic behavior, 3) There are strong decreasing trends in the monthly precipitation tendencies in January and February far away from the no-trend line (1:1, 45°). The same is valid in the sequence of June-July-August months but in opposite direction at weaker decreasing rate, 4) Starting from February onwards there is a sharp transition from the decreasing part to increasing part of the IPTA template towards March and then onwards remains in the same part during transitions to the subsequent month. There is a decreasing tendency from May to the limb mentioned in the previous step, 5) From August to September there is again a transition to increasing trend region and then after December to the decreasing region until January, 6) Finally, maximum values of trend lengths are calculated as 36,1 (mm), and 26,2 (mm) for mean and standard deviation respectively. Also, maximum values for trend slope are calculated as 117,3 and
Old (1st) half sub-series Fig. 2. A form of trend polygons. 204
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Fig. 3a. Location map of Goksu River Basin.
March and August to September for arithmetic mean graph, 2) There are also transitions from the increase to decrease area from January to February and June to July in the arithmetic mean graph, 3) The previous steps indicate to transitions from winter to spring and from summer to winter season respectively, 4) Since it is a polygon that closes onto itself the region is under the effect of rather a systematic weather transition with almost stable stages, 5) There are strong increasing trends in the standard deviations of monthly precipitation tendencies. All months remain in the increasing trend area, 6) There are strong increasing trends in the monthly precipitation tendencies of standard deviation in January, December, April and June far away from the no-trend line (1:1, 45° straight-line), 7) Finally, maximum values of trend lengths are calculated as 33 (mm), and 17,3 (mm) for mean and standard deviation respectively. Also, maximum values for trend slope are calculated as −316, and 443,2 for mean and standard deviation respectively.
Fig. 3b. Location map of New Jersey (USA).
As for the southern region precipitation monthly arithmetic averages and standard deviation in Fig. 6, again there is not a distinctive polygon that closes onto itself, but rather transitions from increase to decrease areas and vice versa. The following points are among the most significant features of precipitation IPTA template behavior from the Fig. 6 and Table 3 for the southern region 1) Although from January to February, there is a complete decreasing trend, but from February to March there is a significant transition from trend decrease area to the increase area for arithmetic mean graph, 2) As for Fig. 6 arithmetic mean, after March two more months, the trend remains in increasing form with decreasing trends, but another significant transition takes place from May to June and remain there for the next two more months, 3) The transition from August to September in arithmetic mean is another lengthy trend and the following three months are also in the increasing region, 4) The final segment of the IPTA approach is from increase to trend decrease area, and hence the polygon reaches to January, 5) Finally, maximum values of trend lengths are calculated as 17,3 (mm), and 15,2 (mm) for mean and standard deviation, respectively. Also, maximum values for trend slope are calculated as 443,2, and −415 for mean and standard deviation respectively.
Fig. 3c. Location map of Danube River (Romania).
2683 for mean and standard deviation respectively. Apart from the above linguistic interpretations the numerical values are given in Table 1, which provides useful information for any quantitative study. Fig. 5 indicates the precipitation monthly arithmetic average and standard deviation transitions for the northern region, where some linguistic points are completely different the previous one. Table 2 presents numerical values of the northern regions IPTA. One can infer the following major points from the Fig. 5 and Table 2 for the northern region of the New Jersey state.
Fig. 7 is the last IPTA template of the whole statewide precipitation pattern of New Jersey, which implies the following significant points about the precipitation arithmetic average and standard deviation polygon. Also, Table 4 summarizes the numerical values of these graphs.
1) There is a distinctive polygon, where only three months, namely, February, July and August appear in the decreasing trend area with transitions towards the increasing trend area from February to 205
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Fig. 4. IPTA graph for New Jersey coastal region precipitation records for Table 1.
Fig. 5. IPTA graph for New Jersey northern region precipitation records for Table 2.
Fig. 6. IPTA graph for New Jersey southern region precipitation records for Table 3.
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Fig. 7. IPTA graph for New Jersey statewide region precipitation records for Table 4. Table 1 IPTA monthly statistical values of arithmetic mean and standard deviation graph in Fig. 4. New Jersey (Coastal region)
Mean Standard deviation
Months
1st half (mm) 2nd half (mm) 1st half (mm) 2nd half (mm)
(Coastal region) Mean Standard deviation
Trend Trend Trend Trend
length (mm) slope length (mm) slope
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
92,2 84,8 30,5 40,1
88,1 78,5 33,5 33,5
95,8 103,1 33,3 42,4
83,8 90,4 27,9 37,3
76,7 85,1 36,3 41,9
83,3 78,2 32,3 36,3
101,1 98,3 53,8 51,3
111,8 109,2 54,6 51,6
84,3 85,6 53,1 41,7
81,5 86,9 42,9 46,0
76,2 85,6 43,2 44,2
87,1 94,0 35,3 45,7
Jan Feb
Feb Mar
Mar Apr
Apr May
May Jun
Jun Jul
Jul Aug
Aug Sep
Sep Oct
Oct Nov
NovDec
DecJan
7,6 33,3 7,1 0,3
25,7 −19,8 8,9 2683
17,5 21,6 7,4 25,7
8,6 33,3 9,4 15,7
9,7 −15,5 6,9 18,5
26,9 13,5 26,2 −16,3
15,0 23,4 0,8 27,4
36,1 −11,7 10,2 102,9
3,3 117,3 10,9 −6,6
5,3 43,7 1,8 9,7
13,7 18,8 7,9 234
10,4 23,6 7,4 27,4
Table 2 IPTA monthly statistical values of arithmetic mean and standard deviation graph in Fig. 5. New Jersey (Northern region)
Mean Standard deviation
1st half (mm) 2nd half (mm) 1st half (mm) 2nd half (mm)
(Northern region) Mean Standard deviation
Trend Trend Trend Trend
length (mm) slope length (mm) slope
Months Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
85,1 87,4 30,7 48,0
80,0 75,2 29,5 31,5
95,8 104,4 35,3 46,2
94,2 104,9 36,8 50,0
95,3 103,6 45,2 51,3
101,9 104,4 40,1 53,1
123,7 113,0 52,8 56,4
113,5 112,8 51,3 58,9
97,8 110,0 53,1 58,4
90,7 102,1 54,6 62,0
82,0 98,6 46,0 47,0
86,9 99,1 34,8 51,1
Jan Feb
Feb Mar
Mar-Apr
Apr-May
May-Jun
Jun-Jul
Jul-Aug
Aug-Sep
Sep-Oct
Oct-Nov
Nov-Dec
Dec-Jan
13,2 −48,8 16,8 3,0
33,0 −47,8 16,0 136,1
1,5 31,0 4,1 30,5
1,8 19,8 8,4 11,7
6,6 7,4 5,6 54,4
23,6 −112,5 13,2 7,1
10,2 2,3 2,8 52,8
16,0 −316,0 1,8 17,8
10,9 23,9 4,1 35,6
9,1 36,3 17,3 3,3
4,8 18,8 11,9 443,2
11,7 125,7 5,1 23,9
1) Again, there are decreasing trend starts from January to February then a long transition to the increase area until May, 2) Likewise, the trend components remain in the decrease area for June-July-August month chain, 3) Finally, maximum values of trend lengths are calculated as 33 (mm), and 13,5 (mm) for mean and standard deviation respectively. Also, maximum values for trend slope are calculated as 253,2, and 4053,8 for mean and standard deviation respectively.
The IPTA template in Fig. 8 for arithmetic mean of Danube River has a regular polygon with two limbs as decreasing trends starting from May to October and then a rising limb from November to April. There are also transitions from the increase to decrease area and vice versa in arithmetic mean as in Fig. 8. Table 5 summarizes the numerical values of these graphs. As mentioned earlier in the case of runoff the arithmetic average IPTA templates have almost a single loop polygon. The following points appear as significant features.
This trend polygon is almost similar to New Jersey mean monthly precipitation at southern region.
1) Again, there are decreasing trends start from May to October then a 207
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Table 3 IPTA monthly statistical values of arithmetic mean and standard deviation graph in Fig. 6. New Jersey (Southern region)
Mean Standard deviation
1st half (mm) 2nd half (mm) 1st half (mm) 2nd half (mm)
(Southern region) Mean Standard deviation
Trend Trend Trend Trend
length (mm) slope length (mm) slope
Months Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
30,7 48,0 29,2 40,6
29,5 31,5 33,8 33,0
35,3 46,2 36,1 46,2
36,8 50,0 33,0 39,6
45,2 51,3 40,1 41,1
40,1 53,1 37,1 40,4
52,8 56,4 48,0 50,8
51,3 58,9 56,4 55,6
53,1 58,4 51,8 48,8
54,6 62,0 49,3 47,2
46,0 47,0 41,4 47,8
34,8 51,1 33,5 50,0
Jan-Feb
Feb-Mar
Mar-Apr
Apr-May
May-Jun
Jun-Jul
Jul-Aug
Aug-Sep
Sep-Oct
Oct-Nov
Nov-Dec
Dec-Jan
16,8 3,0 8,9 −1,3
16,0 136,1 13,5 −415,0
4,1 30,5 7,4 16,8
8,4 11,7 7,1 4,1
5,6 54,4 3,0 73,9
13,2 7,1 15,2 22,6
2,8 52,8 9,4 −8,1
1,8 17,8 8,1 86,4
4,1 35,6 3,0 17,0
17,3 3,3 7,9 −77,2
11,9 443,2 8,4 69,3
5,1 23,9 10,4 36,6
Table 4 IPTA monthly statistical values of arithmetic mean and standard deviation graph in Fig. 7. New Jersey (Statewide)
Mean Standard deviation
Months
1st half (mm) 2nd half (mm) 1st half (mm) 2nd half (mm)
(Statewide) Mean Standard deviation
Trend Trend Trend Trend
length (mm) slope length (mm) slope
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
88,1 86,9 29,2 42,4
82,8 75,9 31,5 31,5
97,3 105,4 34,5 43,9
90,2 98,3 33,3 41,7
89,7 95,8 40,9 43,7
97,0 95,5 36,8 42,7
117,3 111,5 48,5 49,0
117,3 113,3 52,3 52,6
92,5 100,1 49,8 49,3
87,6 94,5 50,0 51,1
79,8 92,5 42,7 46,0
86,6 97,3 33,0 49,0
Jan-Feb
Feb-Mar
Mar-Apr
Apr-May
May-Jun
Jun-Jul
Jul-Aug
Aug-Sep
Sep-Oct
Oct-Nov
Nov-Dec
Dec-Jan
12,2 164,6 11,4 0,0
33,0 −29,2 12,7 4053,8
10,2 25,4 2,5 22,9
2,8 19,1 7,9 8,4
7,4 −6,6 4,3 54,9
25,9 94,2 13,5 2,5
1,8 17,0 5,1 12,2
27,9 −48,0 4,1 −55,4
7,6 23,1 1,8 −42,2
8,1 47,0 9,1 83,1
8,4 21,6 10,2 128,3
10,4 253,2 7,4 30,2
Fig. 8. IPTA graph for Danube River runoff records for Table 5.
2)
3) 4) 5)
transition to the increase area until April for arithmetic mean trend polygon figure, There is a distinctive polygon in standard deviation figure, where only four months, namely, December, January, May and June show in the decreasing trend area with transitions towards the increasing trend area from January to February and June to July, There are also transitions from the increase to decrease area from November to December and April to May, In the decreasing trend region of the IPTA template, there is very close slope trend from May to September in the arithmetic average template, The maximum trend length component appears during February-
March duration in the arithmetic mean and October-November in the standard deviation, 6) Finally, maximum values of trend lengths are calculated as 2061 (m3/s), and 678 (m3/s) for mean and standard deviation respectively. Also, maximum values for trend slope are calculated as 4,27 and 7,19 for mean and standard deviation respectively. Finally, Göksu River IPTA template in Fig. 9 has a trend polygon, but this time almost with one limb in arithmetic mean trend polygon, where the limb remains in the trend decrease region completely, but practically very close to the 1:1 (45°) no trend straight-line. On the other hand, the standard deviation for Göksu River IPTA template in 208
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Table 5 IPTA monthly statistical values of arithmetic mean and standard deviation graph in Fig. 8. Danube River
Mean Standard deviation
Months
3
1st half (m /sec) 2nd half (m3/sec) 1st half (m3/sec) 2nd half (m3/sec)
Danube River Mean Standard deviation
Trend Trend Trend Trend
3
volume (m /sec) slope volume (m3/sec) slope
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
4662 4973 1979 1780
4809 5363 1626 1702
6382 6695 1776 2005
7772 7944 2084 2204
7928 7441 1980 1920
6928 6431 1776 1675
5766 5407 1475 1697
4682 4355 1317 1465
4161 3852 1212 1220
4161 3945 1309 1371
4792 4850 1764 1874
5032 5282 1843 1760
Jan-Feb
Feb-Mar
Mar-Apr
Apr-May
May-Jun
Jun-Jul
Jul-Aug
Aug-Sep
Sep-Oct
Oct-Nov
Nov-Dec
Dec-Jan
418 1,78 362 0,38
2061 0,56 338 3,00
1870 0,55 367 0,52
527 −2,83 302 −0,51
1422 1,02 319 1,67
1549 0,72 302 −2,19
1510 0,91 281 0,67
724 0,94 267 0,06
93 0,70 180 7,19
1104 −0,27 678 1,79
494 4,27 139 −0,76
483 0,80 137 0,42
Fig. 9. IPTA graph for Goksu Himmetli River runoff records for Table 6. Table 6 IPTA monthly statistical values of arithmetic mean and standard deviation graph in Fig. 9. Göksu River
Mean Standard deviation
Months
1st half (m3/sec) 2nd half (m3/sec) 1st half (m3/sec) 2nd half (m3/sec)
Göksu River Mean Standard deviation
Trend Trend Trend Trend
volume (m3/sec) slope volume (m3/sec) slope
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
16,53 14,06 5,91 2,77
17,22 17,18 5,91 6,64
22,74 22,37 12,21 9,94
26,17 24,21 16,15 13,40
33,14 27,99 17,36 13,35
57,24 54,75 20,20 26,95
73,24 73,44 22,71 32,82
47,44 46,82 12,66 19,21
28,92 26,00 6,86 7,39
20,41 17,26 3,65 4,08
16,87 14,23 2,68 2,86
15,63 13,64 2,18 2,52
Jan-Feb
Feb-Mar
Mar-Apr
Apr-May
May-Jun
Jun-Jul
Jul-Aug
Aug-Sep
Sep-Oct
Oct-Nov
Nov-Dec
Dec-Jan
3,20 0,01 3,86 −0,23
7,58 10,88 7,11 −3,14
3,89 5,32 5,25 1,21
7,94 2,63 1,21 1,46
36,02 0,48 13,89 −1,68
24,59 −0,08 6,38 1,50
37,07 −3,11 16,91 0,65
27,86 4,71 13,17 0,08
12,20 1,08 4,61 0,83
4,66 0,84 1,57 0,42
1,37 0,75 0,60 1,84
0,99 0,81 3,73 −0,11
Fig. 9 has a trend polygon again with two limbs, where the lower limb remains in the trend decrease region completely and the upper limb is in the increase region of the template. Besides, Table 6 summarizes the numerical values of these graphs. One can deduce the following points from Fig. 9.
3) There is a sharp transition from the trend decrease region to the increase area from May to June, whereas the transition from December to January is rather smooth close to the lowest point in the standard deviation template, 4) Maximum values of trend lengths are calculated as 37,07 (m3/s), and 16,91 (m3/s) for mean and standard deviation respectively. Also, maximum values for trend slope are calculated as 10,88 and −3,14 for mean and standard deviation respectively.
1) The increasing trend segments in standard deviation graph start from June and continues up to December during which July-August part has the biggest trend slope and length, 2) The February-March duration in arithmetic mean has parallel trend to no-trend line (1:1 −45°), 209
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frequency–intensity–duration (FID) curves for Florya station, Istanbul. J. Flood Risk Manage. 11, S403–S418. https://doi.org/10.1111/jfr3.12229. Güçlü, Y.S., Dabanlı, Şişman, E., Şen, Z., 2018b. In: Air Quality (AQ) Identification by Innovative Trend Diagram and AQ Index Combinations in Istanbul Megacity. Atmospheric Pollution Research. Elsevier B.V. https://doi.org/10.1016/j.apr.2018. 06.011. Jones, J.R., Schwartz, J.S., Ellis, K.N., Hathaway, J.M., Jawdy, C.M., 2015. Temporal variability of precipitation in the Upper Tennessee Valley. J. Hydrol.: Reg. Stud. 3, 125–138. https://doi.org/10.1016/j.ejrh.2014.10.006. Kendall, M. G., 1975. Rank Correlation Methods. Charles Griffin (p. 202). Korhonen, J., Kuusisto, E., 2010. Long-term changes in the discharge regime in Finland. Hydrol. Res. 41 (3–4), 253. https://doi.org/10.2166/nh.2010.112. Kyselý, J., 2009. Trends in heavy precipitation in the Czech Republic over 1961–2005. Int. J. Climatol. 29 (12), 1745–1758. https://doi.org/10.1002/joc.1784. Mann, H., 1945. Mann Nonparametric test against trend. Econometrica 13, 245–259. Mohorji, A.M., Şen, Z., Almazroui, M., 2017. Trend analyses revision and global monthly temperature innovative multi-duration analysis. Earth Syst. Environ. 1 (1). https:// doi.org/10.1007/s41748-017-0014-x. Reihan, A., Kriauciuniene, J., Meilutyte-Barauskiene, D., Kolcova, T., 2012. Temporal variation of spring flood in rivers of the Baltic States. Hydrol. Res. 43 (4), 301. https://doi.org/10.2166/nh.2012.141. Sayemuzzaman, M., Jha, M.K., 2014. Seasonal and annual precipitation time series trend analysis in North Carolina, United States. Atmos. Res. 137, 183–194. https://doi.org/ 10.1016/j.atmosres.2013.10.012. Sen, P.K., 1968. Estimates of the regression coefficient based on Kendall’s Tau. J. Am. Stat. Assoc. 63 (324), 1379–1389. https://doi.org/10.1080/01621459.1968. 10480934. Şen, Z., 2012. Innovative trend analysis methodology. J. Hydrol. Eng. 17 (9), 1042–1046. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000556. Şen, Z., 2014. Trend identification simulation and application. J. Hydrol. Eng. 19 (3), 635–642. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000811. Şen, Z., 2017a. Innovative trend significance test and applications. Theor. Appl. Climatol. 127 (3–4), 939–947. https://doi.org/10.1007/s00704-015-1681-x. Şen, Z., 2017b. In: Innovative Trend Methodologies in Science and Engineering. Springer International Publishing, pp. 1–349. https://doi.org/10.1007/978-3-319-52338-5. Sonali, P., Nagesh Kumar, D., 2013. Review of trend detection methods and their application to detect temperature changes in India. J. Hydrol. 476, 212–227. https://doi. org/10.1016/j.jhydrol.2012.10.034. Swain, S., Verma, M., Verma, M.K., 2015. Statistical trend analysis of monthly rainfall for Raipur District, Chhattisgarh. Int. J. Adv. Eng. Res. Stud. IV (II), 87–89. Tabari, H., Taye, M.T., Onyutha, C., Willems, P., 2017. Decadal analysis of river flow extremes using quantile-based approaches. Water Resour. Manage. 31 (11), 3371–3387. https://doi.org/10.1007/s11269-017-1673-y. Theil, H., 2011. A rank-invariant method of linear and polynomial regression analysis. Adv. Stud. Theoret. Appl. Econom. 345–381. https://doi.org/10.1007/978-94-0112546-8_20. Wilson, D., Hisdal, H., Lawrence, D., 2010. Has streamflow changed in the Nordic countries? - Recent trends and comparisons to hydrological projections. J. Hydrol. 394 (3–4), 334–346. https://doi.org/10.1016/j.jhydrol.2010.09.010. Wu, H., Qian, H., 2017. Innovative trend analysis of annual and seasonal rainfall and extreme values in Shaanxi, China, since the 1950s. Int. J. Climatol. 37 (5), 2582–2592. https://doi.org/10.1002/joc.4866. Yu, Y.S., Zou, S., Whittemore, D., 1993. Non-parametric trend analysis of water quality data of rivers in Kansas. J. Hydrol. 150 (1), 61–80. https://doi.org/10.1016/00221694(93)90156-4. Zhang, A., Zheng, C., Wang, S., Yao, Y., 2015. Analysis of streamflow variations in the Heihe River Basin, northwest China: trends, abrupt changes, driving factors and ecological influences. J. Hydrol.: Reg. Stud. 3, 106–124. https://doi.org/10.1016/j. ejrh.2014.10.005.
The main purpose of this paper is to propose a trend assessment method on monthly basis by means of a new concept of Innovative Polygonal Trend Analysis (IPTA), which is another version of the Innovative Trend Analysis (ITA) as it is already available in the literature. Herein, IPTA is used, where there are 12 scatter points on the template each for a month with values of arithmetic averages and standard deviations as the necessity requirements for its preparation. The IPTA template provides much practically demandable linguistic and numerical information such as the trends between two successive months, their slopes and lengths, per month amounts, homogeneities, isotropies, and others. The application of the IPTA is performed for three hydro-meteorological records from different parts of the world including New Jersey (USA), Danube River (Romania) and Göksu River (Turkey) in terms of precipitation and runoff. Declaration of Competing Interest None. References Alashan, S., 2018a. An improved version of innovative trend analyses. Arabian J. Geosci. 11 (3). https://doi.org/10.1007/s12517-018-3393-x. Alashan, S., 2018b. Data analysis in nonstationary state. Water Resour. Manage. 32 (7), 2277–2286. https://doi.org/10.1007/s11269-018-1928-2. Almazroui, M., Şen, Z., Mohorji, A.M., Islam, M.N., 2018. Impacts of climate change on water engineering structures in arid regions: case studies in Turkey and Saudi Arabia. Earth Syst. Environ. https://doi.org/10.1007/s41748-018-0082-6. Bari, S.H., Rahman, M.T.U., Hoque, M.A., Hussain, M.M., 2016. Analysis of seasonal and annual rainfall trends in the northern region of Bangladesh. Atmos. Res. 176–177, 148–158. https://doi.org/10.1016/j.atmosres.2016.02.008. Bocheva, L., Marinova, T., Simeonov, P., Gospodinov, I., 2009. Variability and trends of extreme precipitation events over Bulgaria (1961–2005). Atmos. Res. 93 (1–3), 490–497. https://doi.org/10.1016/j.atmosres.2008.10.025. Burn, D.H., 1994. Hydrologic effects of climatic change in west-central Canada. J. Hydrol. 160 (1–4), 53–70. https://doi.org/10.1016/0022-1694(94)90033-7. Dabanlı, İ., Şen, Z., Yeleğen, M.Ö., Şişman, E., Selek, B., Güçlü, Y.S., 2016. Trend assessment by the innovative-Şen method. Water Resour. Manage. 30 (14), 5193–5203. https://doi.org/10.1007/s11269-016-1478-4. Dabanli, I., Şen, Z., 2018. Classical and innovative-Şen trend assessment under climate change perspective. Int. J. Global Warming 15 (1). https://doi.org/10.1504/IJGW. 2018.091951. Davis, J.C., 2002. In: Statıstıcs and Data Analysis in Geology, third ed. John Wiley and Sons, Inc, pp. 257. https://doi.org/10.1016/j.otohns.2007.09.010. Elouissi, A., Şen, Z., Habi, M., 2016. Algerian rainfall innovative trend analysis and its implications to Macta watershed. Arabian J. Geosci. 9 (4). https://doi.org/10.1007/ s12517-016-2325-x. Güçlü, Y.S., 2018. Multiple Şen-innovative trend analyses and partial Mann-Kendall test. J. Hydrol. https://doi.org/10.1016/j.jhydrol.2018.09.034. Güçlü, Y.S., Şişman, E., Yeleğen, M., 2018a. Climate change and
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Research papers
Innovative Polygon Trend Analysis (IPTA) and applications Zekâi Şen a b
a,b
a,b,⁎
, Eyüp Şişman
a,b
, Ismail Dabanli
T
Istanbul Medipol University, School of Engineering and Natural Sciences, Civil Engineering Department, Kavacık, 34181 Istanbul, Turkey Istanbul Medipol University, Climate Change Researches Application and Research Center, (IKLIMER) Kavacık, 34181 Istanbul, Turkey
ARTICLE INFO
ABSTRACT
This manuscript was handled by Huaming Guo, Editor-in-Chief, with the assistance of Philippe Negrel, Associate Editor
Trend analysis is continuously in the research and application agenda due to climate change effect searches on various engineering, social, economic, agriculture, environmental and water resources design, management, operation and management studies. Classical trend analysis is useable for holistic trend identification and then statistical quantification as for its intercept and slope. The main drawbacks in these classical approaches are the set of fundamental assumptions such as the serial independence of the given time series, pre-whitening, normality of the data and non-existence of serial comparison among different sections of the same record. This paper explains a non-parametric approach to avoid almost all these difficulties by simple methodology, which is referred as the Innovative Polygonal Trend Analysis (IPTA). Such an approach helps not only to identify the trend in a given series, but also trend transitions between successive sections of the two equal segments from the original hydro-meteorological time series leading to trend polygon, which provides a productive basis for finer interpretation with linguistic and numerical interpretations and inferences from a given time series. The application of the IPTA is presented for rainfall records from New Jersey, USA, Danube River and Göksu River discharge records from Romania and Turkey.
Keywords: Hydro-meteorology IPTA Polygon trend Stochastic Time series Trend analysis Trend slope
1. Introduction Hydro-meteorological variable average changes and variabilities in the standard deviation are very essential in different human activities such as water supply, groundwater recharge, hydro-electric energy generation, agricultural activities and irrigation applications. It is expected that recent global warming and consequent climate change impacts may accelerate these changes, and therefore, their control should be done according to objective methodologies. In the literature, there are various methodologies for the assessment of time series trend component and variability changes (Mann, 1945; Sen, 1968; Kendall, 1975; Şen, 2012). A common definition of a trend can be generally directional and in the forms of steadily increasing or decreasing average tendency in a time series. It is possible to recognize such tendencies in a given time series visually. However, their objective identification by scientific and methodological approaches have rather restrictive assumptions. Two implicit features of any trend are its relatively slow average change along time axis and smoothness that it is a continuous straight-line. There may be also non-linear (stochastic) trend components in a hydro-meteorological time series. The purpose of trend analysis is to make future predictions on the objective, quantitative and systematic detection, identification and prediction mechanisms
whereas stochastic component shows itself as the residual around the trend. Such mechanisms are available mostly through the statistical procedures with a set of restrictive basic assumptions. Trend detection analysis has a special place in any statistical analysis of hydro-meteorological, economy, geophysics, quality control, and similar time series studies. Predominantly temporal trends are the main concern, but in some topics especially in geology and engineering works, spatial trend searches are significant for regional assessments. For instance, Trend Surface Analysis (TSA) has been applied by geologists for more than 60 years to separate an observed contour map into two components: a regional trend and a local fluctuation component (Davis, 2002). This approach is limited by using a global polynomial method in trend modeling. It does not allow geologist’s input to achieve an optimal removal of undesirable trend. This leads to a low resolution and sometimes artifacts in highlighting interested features. Climate change and global warming have led to a dramatic increase in trend analysis application of hydro-meteorological time series as temperatures, humidity, precipitation, evaporation, stream flow. The number of trend researches has been increased since the pioneering works of Mann (1945) and Kendall (1975), the couple of which is referred classically as the Mann-Kendal (MK) trend test. This method has been applied frequently by many researches (Burn, 1994; Bocheva
⁎ Corresponding author at: Istanbul Medipol University, School of Engineering and Natural Sciences, Civil Engineering Department, Kavacık, 34181 Istanbul, Turkey. E-mail address: [email protected] (E. Şişman).
https://doi.org/10.1016/j.jhydrol.2019.05.028 Received 8 November 2018; Received in revised form 12 April 2019; Accepted 8 May 2019 Available online 10 May 2019 0022-1694/ © 2019 Elsevier B.V. All rights reserved.
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Recent (2nd) half sub-series
et al., 2009; Kyselý, 2009; Korhonen and Kuusisto, 2010; Reihan et al., 2012; Wilson et al., 2010; Jones et al., 2015; Güçlü, 2018; Zhang et al., 2015; Yu et al., 1993). Besides this, Theil (2011) and Sen (1968) investigated Theil-Sen approach for supporting the MK test helps to detect the magnitude of the trend. Applications of this methodology can be seen in papers by Sayemuzzaman and Jha (2014); Swain et al. (2015) and Bari et al. (2016). Şen (2012) proposed Innovative Trend Analysis (ITA) method, which provides trend identification from inductive and deductive perspectives. This innovative non-parametric approach and its severalversions are analyzed by many researches (Dabanli and Şen, 2018; Şen, 2014, 2017; Alashan, 2018a,b; Güçlü et al., 2018a,b; Dabanlı et al., 2016; Sonali and Nagesh Kumar, 2013; Tabari et al., 2017; Wu and Qian, 2017; Elouissi et al., 2016; Mohorji et al., 2017; Almazroui et al., 2018). Trend detection in holistic manner by aforementioned parametric and non-parametric methods is important, but they do not reflect periodical, say monthly, trend features, which is very essential for depiction of seasonal trend behaviors. Especially, seasonal trend detection can help to regulate or manage water resources systems, agriculture and irrigation works. Therefore, new approach is suggested by evolving ITA procedure to fulfill this gap in trend analysis. The goals of this paper are to explain procedures of IPTA templates and to present its applications for discussions. Such a trend approach provides physical aspects of average and standard deviation seasonal variations that are essential and refined parts hidden in holistic annual trend behaviors. The templates that show transitional trend components between successive months are presented for different hydrometeorological records in Turkey, Romania and United States.
May
Dec Old (1st) half sub-series Fig. 1. A hypothetical Innovative Polygon Trend Analysis (IPTA) template for monthly records.
It is possible to consider this matrix in two halves as the upper (the first) and lower (the second) parts by consideration of the indicator i as i = 1, 2, …, n/2, and i = n/2 + 1, n/2 + 2, … n, respectively. Subsequently, one can calculate the monthly averages and the standard deviations from each half matrix columns as upper half ( x u,2 , x u,2 , , x u,12) , and lower half ( xl,2 , xl,2 , , xl,12 ) and likewise the standard deviations as (su,1, su,2 ,su,12) , and (sl,1, sl,2 ,sl,12 ) , respectively. In the same way it is possible to identify the maximum and minimum values for the upper and lower parts as (M1, M2, , M12), and (m1, m , , m12 ), respectively. Provided that these parameters are considered in two sets then the IPTA version of the ITA template appears as in Fig. 1, where each month is shown as the vertex of the polygon. Successive monthly points are connected by straight-lines, which indicate the transition from one month to the next one. A straight-line provides a set of qualitative and quantitative trend information. The scatter of monthly values in this graph is dependent on the effects of different hydro-meteorological phenomena such as storm types, frequency and magnitude, weather patterns, morphology, human settlement, vegetation, land use and land change. In a regular polygon, there is generally a rising limb followed by a falling sequence. For instance, in the Fig. 1 starting from January (Jan) through points February (Feb), March (Mar), April (Apr), May (May), up to June (Jun), the monthly values are in rise. On the other hand, starting from June (Jun) through July (Jul), August (Aug), September (Sep), October (Oct), November (Nov), December (Dec), and ending in January (Jan), a falling sequence exists. The comparative difference between the rising and recession limbs also provides how the internal change in the concerned hydro-meteorological variable changes. For instance, during the rising sequence, there are more frequent and abundant rainfall occurrences, whereas along the falling sequence opposite situations take place. Although the template in this figure provides rather systematic polygons with one loop, however depending on the physical circumstances, there may be two or even more complex loops. Physically, the more dynamic and chaotic a hydro-meteorological event, the more complex polygon are tending to appear. However, in the case of regular
2. Methodology It is by now well-known that the ITA as suggested by Şen (2012, 2014, 2017a,b) provides visual interpretations and numerical quantifications of a given hydro-meteorological data set classification into “Low”, “Medium” and “High” groups. If necessary one can apply the same technique for two, three or more sub-series of equal length from the mother time series. In the application of ITA, there is no restrictive assumption, which first provides subjective visual interpretations leading to objective linguistic inferences. The slope and intercept of the monotonic trend can be calculated numerically, and finally, the significance test can be applied (Şen, 2017a). IPTA can be applied on several time scales (i.e. daily, monthly, annual…etc). In case of monthly statistical parameters, basically arithmetic average and standard deviation are taken as template construction between 12 set of each parameter from the first half of the mother time series versus to the second part 12 monthly values. These twelve values can also be adapted for any other monthly value such as the skewness coefficient, maximum or minimum, which provide further detailed information about the monthly variations within the data. Although in this paper monthly records are considered, it is possible to expand such a procedure to weekly or even daily data treatment in the same manner. Let us consider a monthly hydro-meteorological time series as x1, x2, …, xn, where n is the number years. This sequence can be arranged into a monthly matrix as,
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phenomenon, the polygons end up with a single loop. For instance, rainfall events might have comparatively more polygonal loops than runoff, because after all the runoff discharges are rather dampened loops due to the collective behavior of a drainage area. In the scatter diagram for monthly records, the straight-lines appear as a 12-vertice polygon with different side lengths and slopes. In general, simply a straight-line expression can be obtained after knowing the coordinates of each successive scatter points on the IPTA template; hence each trend line slope can be calculated. Holistically, IPTA template appears in the form of 12-sided non-linearity within the monthly hydro-meteorological time series. Furthermore, a IPTA template for monthly records provides a basis for qualitative and quantitative interpretations and calculations about the hydro-meteorological system leading to the following useful information:
and upper limits of expected hydro-meteorological variable monthly amounts variation domain. Similarly, any vertical line depicts the lower and upper limits as well as the range of hydrometeorological amount, (h) The smaller the area of the polygon, the more consistent the monthly precipitation and the more stable the hydro-meteorological event occurrence, (i) The smaller the overall slope of the polygon from the horizontal axis, the more intensive the hydro-meteorological event occurrence, (j) In any water resources project planning, operation, maintenance and development the IPTA template provides values for an effective and systematic assessment. These general characteristics of the polygon diagrams reflect many quantitative and qualitative properties of the hydro-meteorological phenomena.
(a) The straight-line between two consecutive months indicates the change in the monthly values. The closed polygon implies the natural balance behavior of the hydro-meteorological variable concerned for one year, (b) The consecutive monthly changes are represented by the length of each straight-line length, (c) If the slope of each straight-line in the IPTA template is close enough to each other both in vertical and horizontal direction, it implies that the relative monthly rates contribute insignificantly to the mean of hydro-meteorological variation for each consecutive month. Likewise, all the straight-lines in the IPTA template first provide explanation on annual basis 12-month variation for qualitative (linguistic) inference at each record location, (d) Each polygon side implies the assumption that there is a linear change between consecutive months. The linearity assumption smaller than one-year implies more realistic results in the trend analysis, (e) If the slopes of all the straight-lines in an IPTA template are not different from each other, all of the sides appear around a single global direction then connection of the polygon vertices provide a broken line, which is very close to the global regression line fit. In this case, the polygon is very narrow, which means that the internal change within the hydro-meteorological variable is quite homogenous, isotropic and has uniform variation behavior, whereas comparatively wider polygons indicate heterogeneous temporal variation, (f) In general, any polygon with a rising form implies that the prevailing conditions are almost in balance. On the contrary, there may arise two or more polygons (loops) rather than a single one as indicated in Fig. 2. (g) Any horizontal line intersection with the polygon provides lower
3. Application The application of the IPTA concept principles is given for three hydro-meteorological monthly records from different parts of the world. These are the New Jersey (USA), where very long precipitation records are available from 1895 up to 2010, Danube River (Romania) monthly flows from 1882 up to 2000 and runoff records from Göksu River (Turkey) from 1936 up to 2000. The locations of each region are presented in Figs. 3a, 3b and 3c. In all the IPTAPTA template graphs in Figs. 4–7 are related to various New Jersey monthly precipitation records. There are significant differences as for the statewide, coastal, northern and southern regions. Table 1 presents numerical values of mean and standard deviation for coastal regions for the first and second halves sub-series in addition to the trend lengths and slopes. For instance, in arithmetic mean figure, individually five of the months (January, February, June, July and August remain below the 1:1 (45°) no trend straight-line, which implies that there were less rainfall monthly averages during the recent half (1953–2010) than the first half (1985–1952). However, in other months, the opposite situation is valid, i.e. there are rainfall increments. Especially, September, October, November, December, April and March periods have rather very complicated and inconsistent rainfall behaviors. Similarly, in standard deviation IPTA graph July, August and September appear under the 1:1 line, indicating that there are tendencies towards decreasing trends, whereas increasing trends are valid in other months. The following points are significant in the interpretation of the monthly arithmetic averages and standard deviation scatters and tables.
Recent (2nd) half sub-series
1) Since there is no regular and stable appearance of successive monthly points as it is usually expected like the polygon in Fig. 1. The mean monthly precipitation and standard deviation at the coastal region of New Jersey state are not stable, because there are non-systematic shifts from month to month, 2) The precipitation phenomenon in this region does not reflect homogeneous and isotropic behavior, 3) There are strong decreasing trends in the monthly precipitation tendencies in January and February far away from the no-trend line (1:1, 45°). The same is valid in the sequence of June-July-August months but in opposite direction at weaker decreasing rate, 4) Starting from February onwards there is a sharp transition from the decreasing part to increasing part of the IPTA template towards March and then onwards remains in the same part during transitions to the subsequent month. There is a decreasing tendency from May to the limb mentioned in the previous step, 5) From August to September there is again a transition to increasing trend region and then after December to the decreasing region until January, 6) Finally, maximum values of trend lengths are calculated as 36,1 (mm), and 26,2 (mm) for mean and standard deviation respectively. Also, maximum values for trend slope are calculated as 117,3 and
Old (1st) half sub-series Fig. 2. A form of trend polygons. 204
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Fig. 3a. Location map of Goksu River Basin.
March and August to September for arithmetic mean graph, 2) There are also transitions from the increase to decrease area from January to February and June to July in the arithmetic mean graph, 3) The previous steps indicate to transitions from winter to spring and from summer to winter season respectively, 4) Since it is a polygon that closes onto itself the region is under the effect of rather a systematic weather transition with almost stable stages, 5) There are strong increasing trends in the standard deviations of monthly precipitation tendencies. All months remain in the increasing trend area, 6) There are strong increasing trends in the monthly precipitation tendencies of standard deviation in January, December, April and June far away from the no-trend line (1:1, 45° straight-line), 7) Finally, maximum values of trend lengths are calculated as 33 (mm), and 17,3 (mm) for mean and standard deviation respectively. Also, maximum values for trend slope are calculated as −316, and 443,2 for mean and standard deviation respectively.
Fig. 3b. Location map of New Jersey (USA).
As for the southern region precipitation monthly arithmetic averages and standard deviation in Fig. 6, again there is not a distinctive polygon that closes onto itself, but rather transitions from increase to decrease areas and vice versa. The following points are among the most significant features of precipitation IPTA template behavior from the Fig. 6 and Table 3 for the southern region 1) Although from January to February, there is a complete decreasing trend, but from February to March there is a significant transition from trend decrease area to the increase area for arithmetic mean graph, 2) As for Fig. 6 arithmetic mean, after March two more months, the trend remains in increasing form with decreasing trends, but another significant transition takes place from May to June and remain there for the next two more months, 3) The transition from August to September in arithmetic mean is another lengthy trend and the following three months are also in the increasing region, 4) The final segment of the IPTA approach is from increase to trend decrease area, and hence the polygon reaches to January, 5) Finally, maximum values of trend lengths are calculated as 17,3 (mm), and 15,2 (mm) for mean and standard deviation, respectively. Also, maximum values for trend slope are calculated as 443,2, and −415 for mean and standard deviation respectively.
Fig. 3c. Location map of Danube River (Romania).
2683 for mean and standard deviation respectively. Apart from the above linguistic interpretations the numerical values are given in Table 1, which provides useful information for any quantitative study. Fig. 5 indicates the precipitation monthly arithmetic average and standard deviation transitions for the northern region, where some linguistic points are completely different the previous one. Table 2 presents numerical values of the northern regions IPTA. One can infer the following major points from the Fig. 5 and Table 2 for the northern region of the New Jersey state.
Fig. 7 is the last IPTA template of the whole statewide precipitation pattern of New Jersey, which implies the following significant points about the precipitation arithmetic average and standard deviation polygon. Also, Table 4 summarizes the numerical values of these graphs.
1) There is a distinctive polygon, where only three months, namely, February, July and August appear in the decreasing trend area with transitions towards the increasing trend area from February to 205
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Fig. 4. IPTA graph for New Jersey coastal region precipitation records for Table 1.
Fig. 5. IPTA graph for New Jersey northern region precipitation records for Table 2.
Fig. 6. IPTA graph for New Jersey southern region precipitation records for Table 3.
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Fig. 7. IPTA graph for New Jersey statewide region precipitation records for Table 4. Table 1 IPTA monthly statistical values of arithmetic mean and standard deviation graph in Fig. 4. New Jersey (Coastal region)
Mean Standard deviation
Months
1st half (mm) 2nd half (mm) 1st half (mm) 2nd half (mm)
(Coastal region) Mean Standard deviation
Trend Trend Trend Trend
length (mm) slope length (mm) slope
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
92,2 84,8 30,5 40,1
88,1 78,5 33,5 33,5
95,8 103,1 33,3 42,4
83,8 90,4 27,9 37,3
76,7 85,1 36,3 41,9
83,3 78,2 32,3 36,3
101,1 98,3 53,8 51,3
111,8 109,2 54,6 51,6
84,3 85,6 53,1 41,7
81,5 86,9 42,9 46,0
76,2 85,6 43,2 44,2
87,1 94,0 35,3 45,7
Jan Feb
Feb Mar
Mar Apr
Apr May
May Jun
Jun Jul
Jul Aug
Aug Sep
Sep Oct
Oct Nov
NovDec
DecJan
7,6 33,3 7,1 0,3
25,7 −19,8 8,9 2683
17,5 21,6 7,4 25,7
8,6 33,3 9,4 15,7
9,7 −15,5 6,9 18,5
26,9 13,5 26,2 −16,3
15,0 23,4 0,8 27,4
36,1 −11,7 10,2 102,9
3,3 117,3 10,9 −6,6
5,3 43,7 1,8 9,7
13,7 18,8 7,9 234
10,4 23,6 7,4 27,4
Table 2 IPTA monthly statistical values of arithmetic mean and standard deviation graph in Fig. 5. New Jersey (Northern region)
Mean Standard deviation
1st half (mm) 2nd half (mm) 1st half (mm) 2nd half (mm)
(Northern region) Mean Standard deviation
Trend Trend Trend Trend
length (mm) slope length (mm) slope
Months Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
85,1 87,4 30,7 48,0
80,0 75,2 29,5 31,5
95,8 104,4 35,3 46,2
94,2 104,9 36,8 50,0
95,3 103,6 45,2 51,3
101,9 104,4 40,1 53,1
123,7 113,0 52,8 56,4
113,5 112,8 51,3 58,9
97,8 110,0 53,1 58,4
90,7 102,1 54,6 62,0
82,0 98,6 46,0 47,0
86,9 99,1 34,8 51,1
Jan Feb
Feb Mar
Mar-Apr
Apr-May
May-Jun
Jun-Jul
Jul-Aug
Aug-Sep
Sep-Oct
Oct-Nov
Nov-Dec
Dec-Jan
13,2 −48,8 16,8 3,0
33,0 −47,8 16,0 136,1
1,5 31,0 4,1 30,5
1,8 19,8 8,4 11,7
6,6 7,4 5,6 54,4
23,6 −112,5 13,2 7,1
10,2 2,3 2,8 52,8
16,0 −316,0 1,8 17,8
10,9 23,9 4,1 35,6
9,1 36,3 17,3 3,3
4,8 18,8 11,9 443,2
11,7 125,7 5,1 23,9
1) Again, there are decreasing trend starts from January to February then a long transition to the increase area until May, 2) Likewise, the trend components remain in the decrease area for June-July-August month chain, 3) Finally, maximum values of trend lengths are calculated as 33 (mm), and 13,5 (mm) for mean and standard deviation respectively. Also, maximum values for trend slope are calculated as 253,2, and 4053,8 for mean and standard deviation respectively.
The IPTA template in Fig. 8 for arithmetic mean of Danube River has a regular polygon with two limbs as decreasing trends starting from May to October and then a rising limb from November to April. There are also transitions from the increase to decrease area and vice versa in arithmetic mean as in Fig. 8. Table 5 summarizes the numerical values of these graphs. As mentioned earlier in the case of runoff the arithmetic average IPTA templates have almost a single loop polygon. The following points appear as significant features.
This trend polygon is almost similar to New Jersey mean monthly precipitation at southern region.
1) Again, there are decreasing trends start from May to October then a 207
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Table 3 IPTA monthly statistical values of arithmetic mean and standard deviation graph in Fig. 6. New Jersey (Southern region)
Mean Standard deviation
1st half (mm) 2nd half (mm) 1st half (mm) 2nd half (mm)
(Southern region) Mean Standard deviation
Trend Trend Trend Trend
length (mm) slope length (mm) slope
Months Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
30,7 48,0 29,2 40,6
29,5 31,5 33,8 33,0
35,3 46,2 36,1 46,2
36,8 50,0 33,0 39,6
45,2 51,3 40,1 41,1
40,1 53,1 37,1 40,4
52,8 56,4 48,0 50,8
51,3 58,9 56,4 55,6
53,1 58,4 51,8 48,8
54,6 62,0 49,3 47,2
46,0 47,0 41,4 47,8
34,8 51,1 33,5 50,0
Jan-Feb
Feb-Mar
Mar-Apr
Apr-May
May-Jun
Jun-Jul
Jul-Aug
Aug-Sep
Sep-Oct
Oct-Nov
Nov-Dec
Dec-Jan
16,8 3,0 8,9 −1,3
16,0 136,1 13,5 −415,0
4,1 30,5 7,4 16,8
8,4 11,7 7,1 4,1
5,6 54,4 3,0 73,9
13,2 7,1 15,2 22,6
2,8 52,8 9,4 −8,1
1,8 17,8 8,1 86,4
4,1 35,6 3,0 17,0
17,3 3,3 7,9 −77,2
11,9 443,2 8,4 69,3
5,1 23,9 10,4 36,6
Table 4 IPTA monthly statistical values of arithmetic mean and standard deviation graph in Fig. 7. New Jersey (Statewide)
Mean Standard deviation
Months
1st half (mm) 2nd half (mm) 1st half (mm) 2nd half (mm)
(Statewide) Mean Standard deviation
Trend Trend Trend Trend
length (mm) slope length (mm) slope
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
88,1 86,9 29,2 42,4
82,8 75,9 31,5 31,5
97,3 105,4 34,5 43,9
90,2 98,3 33,3 41,7
89,7 95,8 40,9 43,7
97,0 95,5 36,8 42,7
117,3 111,5 48,5 49,0
117,3 113,3 52,3 52,6
92,5 100,1 49,8 49,3
87,6 94,5 50,0 51,1
79,8 92,5 42,7 46,0
86,6 97,3 33,0 49,0
Jan-Feb
Feb-Mar
Mar-Apr
Apr-May
May-Jun
Jun-Jul
Jul-Aug
Aug-Sep
Sep-Oct
Oct-Nov
Nov-Dec
Dec-Jan
12,2 164,6 11,4 0,0
33,0 −29,2 12,7 4053,8
10,2 25,4 2,5 22,9
2,8 19,1 7,9 8,4
7,4 −6,6 4,3 54,9
25,9 94,2 13,5 2,5
1,8 17,0 5,1 12,2
27,9 −48,0 4,1 −55,4
7,6 23,1 1,8 −42,2
8,1 47,0 9,1 83,1
8,4 21,6 10,2 128,3
10,4 253,2 7,4 30,2
Fig. 8. IPTA graph for Danube River runoff records for Table 5.
2)
3) 4) 5)
transition to the increase area until April for arithmetic mean trend polygon figure, There is a distinctive polygon in standard deviation figure, where only four months, namely, December, January, May and June show in the decreasing trend area with transitions towards the increasing trend area from January to February and June to July, There are also transitions from the increase to decrease area from November to December and April to May, In the decreasing trend region of the IPTA template, there is very close slope trend from May to September in the arithmetic average template, The maximum trend length component appears during February-
March duration in the arithmetic mean and October-November in the standard deviation, 6) Finally, maximum values of trend lengths are calculated as 2061 (m3/s), and 678 (m3/s) for mean and standard deviation respectively. Also, maximum values for trend slope are calculated as 4,27 and 7,19 for mean and standard deviation respectively. Finally, Göksu River IPTA template in Fig. 9 has a trend polygon, but this time almost with one limb in arithmetic mean trend polygon, where the limb remains in the trend decrease region completely, but practically very close to the 1:1 (45°) no trend straight-line. On the other hand, the standard deviation for Göksu River IPTA template in 208
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Table 5 IPTA monthly statistical values of arithmetic mean and standard deviation graph in Fig. 8. Danube River
Mean Standard deviation
Months
3
1st half (m /sec) 2nd half (m3/sec) 1st half (m3/sec) 2nd half (m3/sec)
Danube River Mean Standard deviation
Trend Trend Trend Trend
3
volume (m /sec) slope volume (m3/sec) slope
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
4662 4973 1979 1780
4809 5363 1626 1702
6382 6695 1776 2005
7772 7944 2084 2204
7928 7441 1980 1920
6928 6431 1776 1675
5766 5407 1475 1697
4682 4355 1317 1465
4161 3852 1212 1220
4161 3945 1309 1371
4792 4850 1764 1874
5032 5282 1843 1760
Jan-Feb
Feb-Mar
Mar-Apr
Apr-May
May-Jun
Jun-Jul
Jul-Aug
Aug-Sep
Sep-Oct
Oct-Nov
Nov-Dec
Dec-Jan
418 1,78 362 0,38
2061 0,56 338 3,00
1870 0,55 367 0,52
527 −2,83 302 −0,51
1422 1,02 319 1,67
1549 0,72 302 −2,19
1510 0,91 281 0,67
724 0,94 267 0,06
93 0,70 180 7,19
1104 −0,27 678 1,79
494 4,27 139 −0,76
483 0,80 137 0,42
Fig. 9. IPTA graph for Goksu Himmetli River runoff records for Table 6. Table 6 IPTA monthly statistical values of arithmetic mean and standard deviation graph in Fig. 9. Göksu River
Mean Standard deviation
Months
1st half (m3/sec) 2nd half (m3/sec) 1st half (m3/sec) 2nd half (m3/sec)
Göksu River Mean Standard deviation
Trend Trend Trend Trend
volume (m3/sec) slope volume (m3/sec) slope
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
16,53 14,06 5,91 2,77
17,22 17,18 5,91 6,64
22,74 22,37 12,21 9,94
26,17 24,21 16,15 13,40
33,14 27,99 17,36 13,35
57,24 54,75 20,20 26,95
73,24 73,44 22,71 32,82
47,44 46,82 12,66 19,21
28,92 26,00 6,86 7,39
20,41 17,26 3,65 4,08
16,87 14,23 2,68 2,86
15,63 13,64 2,18 2,52
Jan-Feb
Feb-Mar
Mar-Apr
Apr-May
May-Jun
Jun-Jul
Jul-Aug
Aug-Sep
Sep-Oct
Oct-Nov
Nov-Dec
Dec-Jan
3,20 0,01 3,86 −0,23
7,58 10,88 7,11 −3,14
3,89 5,32 5,25 1,21
7,94 2,63 1,21 1,46
36,02 0,48 13,89 −1,68
24,59 −0,08 6,38 1,50
37,07 −3,11 16,91 0,65
27,86 4,71 13,17 0,08
12,20 1,08 4,61 0,83
4,66 0,84 1,57 0,42
1,37 0,75 0,60 1,84
0,99 0,81 3,73 −0,11
Fig. 9 has a trend polygon again with two limbs, where the lower limb remains in the trend decrease region completely and the upper limb is in the increase region of the template. Besides, Table 6 summarizes the numerical values of these graphs. One can deduce the following points from Fig. 9.
3) There is a sharp transition from the trend decrease region to the increase area from May to June, whereas the transition from December to January is rather smooth close to the lowest point in the standard deviation template, 4) Maximum values of trend lengths are calculated as 37,07 (m3/s), and 16,91 (m3/s) for mean and standard deviation respectively. Also, maximum values for trend slope are calculated as 10,88 and −3,14 for mean and standard deviation respectively.
1) The increasing trend segments in standard deviation graph start from June and continues up to December during which July-August part has the biggest trend slope and length, 2) The February-March duration in arithmetic mean has parallel trend to no-trend line (1:1 −45°), 209
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4. Conclusions
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The main purpose of this paper is to propose a trend assessment method on monthly basis by means of a new concept of Innovative Polygonal Trend Analysis (IPTA), which is another version of the Innovative Trend Analysis (ITA) as it is already available in the literature. Herein, IPTA is used, where there are 12 scatter points on the template each for a month with values of arithmetic averages and standard deviations as the necessity requirements for its preparation. The IPTA template provides much practically demandable linguistic and numerical information such as the trends between two successive months, their slopes and lengths, per month amounts, homogeneities, isotropies, and others. The application of the IPTA is performed for three hydro-meteorological records from different parts of the world including New Jersey (USA), Danube River (Romania) and Göksu River (Turkey) in terms of precipitation and runoff. Declaration of Competing Interest None. References Alashan, S., 2018a. An improved version of innovative trend analyses. Arabian J. Geosci. 11 (3). https://doi.org/10.1007/s12517-018-3393-x. Alashan, S., 2018b. Data analysis in nonstationary state. Water Resour. Manage. 32 (7), 2277–2286. https://doi.org/10.1007/s11269-018-1928-2. Almazroui, M., Şen, Z., Mohorji, A.M., Islam, M.N., 2018. Impacts of climate change on water engineering structures in arid regions: case studies in Turkey and Saudi Arabia. Earth Syst. Environ. https://doi.org/10.1007/s41748-018-0082-6. Bari, S.H., Rahman, M.T.U., Hoque, M.A., Hussain, M.M., 2016. Analysis of seasonal and annual rainfall trends in the northern region of Bangladesh. Atmos. Res. 176–177, 148–158. https://doi.org/10.1016/j.atmosres.2016.02.008. Bocheva, L., Marinova, T., Simeonov, P., Gospodinov, I., 2009. Variability and trends of extreme precipitation events over Bulgaria (1961–2005). Atmos. Res. 93 (1–3), 490–497. https://doi.org/10.1016/j.atmosres.2008.10.025. Burn, D.H., 1994. Hydrologic effects of climatic change in west-central Canada. J. Hydrol. 160 (1–4), 53–70. https://doi.org/10.1016/0022-1694(94)90033-7. Dabanlı, İ., Şen, Z., Yeleğen, M.Ö., Şişman, E., Selek, B., Güçlü, Y.S., 2016. Trend assessment by the innovative-Şen method. Water Resour. Manage. 30 (14), 5193–5203. https://doi.org/10.1007/s11269-016-1478-4. Dabanli, I., Şen, Z., 2018. Classical and innovative-Şen trend assessment under climate change perspective. Int. J. Global Warming 15 (1). https://doi.org/10.1504/IJGW. 2018.091951. Davis, J.C., 2002. In: Statıstıcs and Data Analysis in Geology, third ed. John Wiley and Sons, Inc, pp. 257. https://doi.org/10.1016/j.otohns.2007.09.010. Elouissi, A., Şen, Z., Habi, M., 2016. Algerian rainfall innovative trend analysis and its implications to Macta watershed. Arabian J. Geosci. 9 (4). https://doi.org/10.1007/ s12517-016-2325-x. Güçlü, Y.S., 2018. Multiple Şen-innovative trend analyses and partial Mann-Kendall test. J. Hydrol. https://doi.org/10.1016/j.jhydrol.2018.09.034. Güçlü, Y.S., Şişman, E., Yeleğen, M., 2018a. Climate change and
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