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Selection of homoclimates based on comparisons with single stations and using monthly rainfall and temperature data
Agricultural Meteorology, 26 (1982) 179--194 Elsevier Scientific Publishing Company, Amsterdam -- Printed in The Netherlands
SELECTION OF HOMOCLIMATES BASED ON COMPARISONS SINGLE STATIONS AND USING MONTHLY RAINFALL AND TEMPERATURE DATA
179
WITH
J.S. RUSSELL
CSIRO, Division of Tropical Crops and Pastures, Cunningham Laboratory, St. Lucia, Qld. 4067 (Australia) (Received January 9, 1980; revision accepted December 30, 1981) ABSTRACT Russell, J.S., 1982. Selection of homoclimates based on comparisons with single stations and using monthly rainfall and temperature data. Agric. Meteorol., 26: 179--194. A method is proposed for the detection of homoclimates using the Canberra metric as a similarity coefficient to assess the large amounts of global monthly rainfall and temperature data, such as is available in Wernstedt (World Climatic Data). The method uses the dimensionless and ratio characteristics of the Canberra metric to compare stations on the basis of numerical climatic attributes. Ranking of the stations from the most similar to least similar to a reference station is carried out, enabling homoclimates to be identified. Analysis of the similarity of temperature, cumulative temperature, rainfall, cumulative rainfall and rainfall/temperature ratio attributes of homoclimates is also carried out. The method is used to compare 349 Mexican and Central American stations with five north Australian reference stations for both the wet season and the whole year. The necessity for defining homoclimates in Mexico and Central America arose from a recent plant collecting expedition to this region which had the objective of broadening the germplasm base of tropical forage legumes suitable for certain areas of northern Australia. The method maximizes the information content of the climatic data available and enables comparative climatic information for different regions of the world to be obtained quickly and cheaply. INTRODUCTION In an earlier paper, the use of pattern analysis to detect homoclimates was described (Russell and Moore, 1970). As an example, homoclimates of the Brigalow region of eastern Australia were found with 130 global stations u s i n g m o n t h l y v a l u e s o f 11 c l i m a t i c a t t r i b u t e s . There are two limitations to this approach. Firstly, the lack of detailed c h m a t i c d a t a in r e g i o n s o f t h e w o r l d w h e r e h o m o c l i m a t e s a r e l i k e l y t o b e r e q u i r e d {such as s u b t r o p i c a l a n d t r o p i c a l a r e a s ) , l i m i t s t h e a p p l i c a b i l i t y o f t h e t e c h n i q u e . S e c o n d l y , t h e c l a s s i f i c a t i o n u s e d r e s u l t s in c o m p u t i n g t i m e increasing by the square of the number of stations considered. This imposes a c o n s t r a i n t o n t h e n u m b e r o f s t a t i o n s t h a t c a n b e e v a l u a t e d in p r a c t i c e . S i n c e t h e o r i g i n a l p a p e r w a s p u b l i s h e d , s o m e p r o g r e s s h a s b e e n m a d e in the consolidation of global climatic data. In particular, the compilation of 0002-1571/82/0000--0000/$02.75
© 1982 Elsevier Scientific Publishing Company
180 m o n t h l y rainfall and temperature data for some 19,000 world stations (Wernstedt, 1972) has provided a valuable source reference. With such a large range o f stations, this source provides an extensive coverage of most countries in the world. However, its usefulness is limited by the fact that only two parameters, mean m o n t h l y rainfall and mean m o n t h l y temperature, are reported. The need to develop a more effective m e t h o d of detecting homoclimates arose as a result of a plant collecting expedition m o u n t e d in 1979 by CSIRO Division of Tropical Crops and Pastures to Mexico and Central America in c o o p e r a t i o n with national governments. This expedition had the task of collecting tropical forage legumes suitable for nort hern Australia environments. South and Central America have already been a valuable source of forage legumes genera such as Stylosanthes, Macroptilium, Desmodium and Centrosema (Hutton, 1970). These introduced legumes form the basis of improved grass--legume pastures in the nort hern Australian tropics and subtropics. The purpose of the expedition was to broaden the germplasm base of genera previously introduced and to search for legumes for specific environmerits where previous introductions have been unsuccessful, such as clay soil areas in north-eastern Australia. Mexico, Guatemala and Honduras were chosen for more intensive study because of their climatic similarity to areas o f n o r th er n Australia and because of past successful introductions from this region. Precise knowledge of similar climatic areas in the search area was thus an i m p o r t a n t planning prerequisite if the expedition was to increase its chances of successful plant collection in the limited time available, particularly as climatic gradients are very steep in parts of Mexico and Central Amercia. To assist in the definition of homoclimates, a modified m e t h o d of comparing single climatic stations was developed. This m e t h o d makes use of the geographically extensive data of Wernstedt (1972) and maximizes the information c o n t e n t of the two climatic parameters available. The m e t h o d uses a similarity coefficient to compare stations but ranking rather than grouping is used to ordinate the stations. Analysis of specific climatic attributes of the homoclimates was also carried out. METHODS
Characteristics o f the Canberra metric The similarity coefficient used was the Canberra metric which was defined by Clifford and Williams (1976) as the ratio of the absolute value of the difference between two attributes over the sum of the two attributes. For any two stations, these ratios are summed over all attributes and the mean value found, i.e.
181
1 Cjk = -- ~_ (Xij -- Xik )/(Xij + Xik ) rl
(1)
i=l
where Cjle is the similarity c o e f f i c i e n t for s t a t i o n s ] and k, Xij is the value of a t t r i b u t e i at station j and Xik is the value of a t t r i b u t e i at station k. n is the n u m b e r o f a t t r i b u t e s used in the c o m p a r i s o n . T h e Canberra metric is useful as a similarity c o e f f i c i e n t for c o m p a r i n g the numerical a t t r i b u t e s o f climatic stations because it is dimensionless and because its value is an i n d i c a t i o n o f the ratio o f the a t t r i b u t e s Xij and Xile. When n = 1 the metric can be expressed as
cj~ = I z - l l / ( z + l )
(2)
where z = X j / X k . T h e relationship b e t w e e n Cjk and z for values o f z ~> 0 is s h o w n in Fig. 1. The C a n b e r r a metric is c o n s t r a i n e d b e t w e e n 0 and 1. When Xj and Xle are equal, z = 1 and Cjle = 0. Similarity b e t w e e n the values o f the a t t r i b u t e s is thus s h o w n by low values o f the metric. There is also a relationship b e t w e e n the value o f the metric and the ratio Xj/Xle i.e. w h e n the ratio X j / X k is 2/1 or 1/2, Cjk = 0 . 3 3 3 ; w h e n the ratio is 3/1 or 1/3, Cjle = 0.5, etc. Thus the value o f the metric is an i n d i c a t i o n o f t h e ratio Xj/XIe. If Xj is greater t h a n X k , i.e. (z -- 1) is positive, t h e n the ratio of X] to X k can be calculated f r o m the value Cjk as follows
Xj/Xle = (1 + Cyk)/(1 --Cjh)
(3)
where Xj is less t h a n X k , i.e. (z -- 1) is negative, t h e n the ratio o f Xj to XIe can be calculated as follows
Xj/Xk = (1 -- Cjk)/(1 + erie)
(4)
Values of the ratio for certain values of the metric are shown in Table I. Where the metric has a value of 0.05 or less, the values of Xj and Xk do not differ by more than 10.5%. Similarly, where the metric has a value of 0.10 or ,0[ 08;
06~ j J J
i
) o2~ i
L_
\,
/
"\
J
/ \',
/
,~/ V a l u e of
Z
Fig. 1. Relationship between the Canberra metric and the value of z, where z is the ratio of the attributes.
182 TABLEI Values of the attribute ratio Xj/Xk for specific values of the Canberra metric, Cjk. Values of the ratio of less than 1 occur where Xj is less than Xk. Values of the ratio of more than 1 are where Xj is greater than Xk Value of Cjk
Value of the ratio X]/Xk
0.05 0.10 0.15 0.20 0.25
0.905 0.818 0.739 0.667 0.600
or or or or or
1.105 1.222 1.353 1.500 1.667
less, the values o f Xj and Xk do n o t differ by m o r e t h a n 22.2%. A t higher values o f the metric, the values o f the ratio X]/Xk b e c o m e larger b u t also b e c o m e m o r e s k e w e d percentage-wise d e p e n d i n g on w h e t h e r Xj is greater or less than Xk.
Comparisons o f stations and attributes used L o c a t i o n s o f the five stations (Katherine, K i m b e r l e y Research Station, Charters Towers, E m e r a l d and N a r a y e n Research Station) in n o r t h e r n Aust: ralia with which h o m o c l i m a t e s were sought, are s h o w n in Table II, and their m e a n m o n t h l y rainfall and t e m p e r a t u r e s are s h o w n in Table III. These stations were each c o m p a r e d with 275, 59 and 15 stations in Mexico, Guatemala and H o n d u r a s , respectively, f o r w h i c h b o t h m o n t h l y rainfall and temp e r a t u r e data were available (Wernstedt, 1972), (These d a t a are given in inches and ° F and were t r a n s f o r m e d into millimetres and °C.) As the rainfall and p l a n t g r o w t h p a t t e r n s in n o r t h e r n Australia are strongly seasonal, separate c o m p a r i s o n s for the f o u r m o n t h wet season ( D e c e m b e r - March) a n d the whole y e a r ( D e c e m b e r - - N o v e m b e r ) were made. Equivalent m o n t h s in the n o r t h e r n h e m i s p h e r e are J u n e - - S e p t e m b e r , and J u n e - - M a y . In a d d i t i o n t o the individual m o n t h l y values o f rainfall, a series o f cumula-
TABLE II Locations of the five reference stations for which homoclimates in Mexico and Central America were sought Station
Latitude (°S)
Longitude (°E)
Altitude (m)
Katherine Kimberley Research Station Charters Towers Emerald Narayen Research Station
14 ° 15 ° 20 ° 23 ° 25 °
132 ° 128 ° 146 ° 148 ° 150 °
108 37 306 175 280
28'S 30'S 4'S 32'S 41'S
18'E 43' E 16'E 10'E 52'E
219
200 132 100
96
190 139 108
107
Katherine Kimberley Research Station Charters T o w e r s Emerald N a r a y e n Research Station
Feb.
201
Jan.
28.8
29.6 27.2 27.1
24.7
29.2
30.2 27.6 27.4
25.4
Mean m o n t h l y t e m p e r a t u r e
Katherine Kimberley Research Station Charters T o w e r s Emerald Narayen R e s e a r c h Station
Rainfall
Station
23.6
29.4 25.8 25.5
28.4
73
116 104 72
164
Mar.
20.5
27.8 23.7 22.8
26.7
37
47 38 34
48
Apr.
16.9
25.2 20.8 18.6
24.0
39
12 20 27
5
May
13.9
22.8 18.2 15.8
21.4
37
3 28 36
2
June
M o n t h l y rainfall ( m m ) a n d m e a n t e m p e r a t u r e (°C) for t h e r e f e r e n c e s t a t i o n s
T A B L E III
13.2
22.2 17.4 14.5
21.1
36
6 16 27
2
July
14.8
24.0 19.6 16.6
23.2
27
1 12 22
1
Aug.
17.3
27.4 22.0 20.0
26.9
34
3 16 24
6
Sept.
21.2
30.6 25.1 24.0
30.5
55
22 19 38
28
Oct.
23.7
31.2 27.1 26.4
31.0
77
62 41 57
79
Nov.
25.2
31.2 27.7 27.2
30.1
101
126 85 86
155
Dec.
20.1
27.7 23.5 22.2
26.8
719
788 650 631
910
G¢ ¢,o
Annual total
184 tive m o n t h l y rainfall and t e m per a t ur e values were calculated for each analysis at each station. The possibility of using empirical t em perat ure relations to estimate m o n t h l y evaporation, and hence m o n t h l y rainfall/evaporation ratios, was considered. However, there can be large errors in estimating evaporation and it was decided to use the simple De Martonne index R / ( T + 10) instead (Gentilli, 1958) where R is rainfall and T is temperature. Thus the mean m o n t h l y value of rainfall (in mm) divided by mean m o n t h l y temperature (°C + 10) was calculated. This index does not p u r p o r t to measure evaporation b u t is a useful indication of the relative m o n t h l y balance on rainfall and evaporation. In all, each station was represented by 18 attributes in the case o f the wet season analysis, and 58 attributes in the case of the whole year analysis. (The 18 attributes comprised 4 m o n t h l y values of rainfall, temperature and de Martonne index respectively, plus 3 values of cumulative rainfall and tem pe r at ur e respectively. The 58 attributes comprised 12 m o n t h l y values o f rainfall etc.)
Application o f the method and assessment of homoclimates Each Australian station was compared with the 349 Mexican and Central American stations for both summer and the whole year over the 18 or 58 attributes respectively, using the Canberra metric. In each analysis the 349 similarity coefficients were then ranked in increasing value. The station with the lowest value had the closest match to the Australian station based on the available data and the m e t h o d used. In addition to calculating an overall value of the Canberra metric, further analyses were carried out to determine the cont ri but i on of the various climatic attributes to the mean value. The following additional information was obtained for each station: (1) Canberra metrics for each station and the reference station were calculated for each climatic attribute over the months considered. Thus, in addition to a single similarity coefficient, values for temperature, cumulative temperature, rainfall, cumulative rainfall and the rainfall/temperature ratio were calculated. The sum of these, weighted in each case for the months over which th ey were calculated, gives the overall Canberra metric used for ranking. (2) The n u m b e r of m ont hs in each comparison where Xj was equal to or greater than X k or less than X k was recorded for each climatic attribute over the m o n t h s considered. This indicated how m any m ont hs had higher or lower temperature, rainfall, etc. than the reference station. {3) Canberra metrics were calculated separately for climatic attributes over all mo n th s considered where Xj was equal to or greater than Xk and where Xj was less than Xk. Fr om the means of these values it was possible to calculate the mean percentage difference of the climatic attribute from the reference site. (4) Maximum values of the Canberra metric were calculated separately for
185
climatic a t t r i b u t e s o v e r all m o n t h s c o n s i d e r e d , w h e r e X] was equal to or greater t h a n Xk a n d w h e r e X] was less t h a n Xk. This allowed the p e r c e n t a g e d i f f e r e n c e o f the m o s t d e v i a n t m o n t h for the climatic a t t r i b u t e to be calculated. This a d d i t i o n a l i n f o r m a t i o n e n a b l e d assessments to be m a d e o f similarities o f the various climatic a t t r i b u t e s of the h o m o c l i m a t e s with the r e f e r e n c e stations. RESULTS A l t h o u g h calculations were carried o u t for all stations, detailed c o m p a r i sons with the ten m o s t similar Mexican and Central A m e r i c a n s t a t i o n s are p r e s e n t e d f o r K a t h e r i n e and the N a r a y e n R e s e a r c h S t a t i o n only. C o m p a r i sons f o r the w e t season and the w h o l e y e a r a n d b o t h the overall similarity c o e f f i c i e n t a n d t h e similarity c o e f f i c i e n t s for specific climatic a t t r i b u t e s are s h o w n in T a b l e s IV and V. T h e analysis s h o w e d n o t o n l y the m o s t similar s t a t i o n s b u t also the relative c o n t r i b u t i o n o f the various climatic a t t r i b u t e s t o the overall similarity c o e f f i c i e n t . In s o m e cases the m o s t similar s t a t i o n was m o s t similar in all a t t r i b u t e s . H o w e v e r , in m a n y cases this was n o t the case. T h u s in the w h o l e y e a r analysis in T a b l e IV, t h e stations Iguala, H u e t a m o a n d Salina Cruz had m o r e similar t e m p e r a t u r e p a t t e r n s t o K a t h e r i n e t h a n P u e n t a de I x t l a b u t this was o f f s e t b y m o r e dissimilar rainfall p a t t e r n s . Likewise, Etla (Table V ) h a d a m o r e similar rainfall p a t t e r n t o N a r a y e n t h a n C h i q u i m u l a b u t this was o f f s e t b y a less similar t e m p e r a t u r e p a t t e r n . A m o r e d e t a i l e d analysis of the climatic a t t r i b u t e s o f the five m o s t similar s t a t i o n s is s h o w n in T a b l e s VI, V I I and V I I I . T a b l e VI indicates the n u m b e r o f m o n t h l y values o f the climatic a t t r i b u t e s equal t o or greater t h a n the r e f e r e n c e s t a t i o n a n d values less t h a n the r e f e r e n c e station. This allows c o m p a r i s o n s o f s t a t i o n s in t e r m s o f w h e t h e r , f o r e x a m p l e , t e m p e r a t u r e or rainfall are c o n s i s t e n t l y a b o v e or b e l o w t h e values f o r the r e f e r e n c e station. T a b l e V I I s h o w s t h e m e a n C a n b e r r a m e t r i c values o f a t t r i b u t e values equal t o o r a b o v e t h e r e f e r e n c e s t a t i o n and t h o s e b e l o w the r e f e r e n c e station. This enables an e s t i m a t e o f the m e a n p e r c e n t a g e v a r i a t i o n o f the a t t r i b u t e c o m p a r e d with the r e f e r e n c e station. T a b l e V I I I indicates the m a x i m u m Canb e r r a m e t r i c f o r the a t t r i b u t e values equal to or a b o v e the r e f e r e n c e s t a t i o n a n d t h o s e b e l o w the r e f e r e n c e station. This enables the p e r c e n t a g e v a r i a t i o n o f t h e m o s t d e v i a n t a t t r i b u t e c o m p a r e d with r e f e r e n c e s t a t i o n t o be determined. T h e d a t a in T a b l e V I I can be used f o r c o n v e r t i n g b a c k t o the relative values o f t h e original a t t r i b u t e s . T h u s f o r H u e t a m o , the C a n b e r r a m e t r i c values f o r t e m p e r a t u r e in c o m p a r i s o n w i t h K a t h e r i n e were 0 . 0 1 3 w h e r e the ratio Xj/Xk was equal to or greater t h a n 1 and 0 . 0 0 3 w h e r e Xj/Xk was less t h a n 1. Using eqs. 3 a n d 4 it can be c a l c u l a t e d t h a t w h e r e m o n t h l y t e m p e r a ture values f o r H u e t a m o were greater t h a n K a t h e r i n e , i.e. (z -- 1) was positire, t h e m e a n d i f f e r e n c e b e t w e e n m o n t h l y t e m p e r a t u r e s was 2.6% Where
Country a
M M M M M G M M M M
M M M M H M M M M M
0.1107 0.1191 0.1290 0.1296 0.1460 0.1537 0.1546 0.1549 0.1559 0.1599
0.0219 0.0318 0.0430 0.0475 0.0507 0.0517 0.0536 0.0548 0.0548 0.0606
Overall similarity c o e f f i c i e n t
a M = Mexico, G = G u a t e m a l a , H = H o n d u r a s
P u e n t e de Ixtla Alcozauca Jonacatepec Chiautla Iguala Amatitlan T u x t l a Gutierrez Huetamo Cintalapa Salina Cruz
Whole year ( J u n e - - M a y )
Huetamo Zirandaro Champoton Soledad Doblado Tela Campeche C a r m e n Ciudad G u e r r e r o Villa Colima Rio M a n t e
Wet season ( J u n e - - S e p t e m b e r )
Station
0.046 0,112 0.093 0.059 0.032 0,056 0,046 0.033 0.068 0.041
0.008 0.007 0,021 0.017 0.039 0.034 0.032 0.016 0.061 0.026
Temp. (°C)
0.205 0.158 0.205 0.236 0,267 0,301 0.312 0.341 0.295 0.316
0.040 0.054 0,070 0.067 0.068 0.067 0.081 0,092 0.060 0,090
Rain (mm)
0.055 0.123 0.107 0.070 0.015 0,056 0,055 0.020 0,075 0.016
0.009 0.007 0.024 0,015 0,043 0,039 0.036 0.019 0.062 0.027
Cum. temp.
0.035 0.034 0.020 0,036 0,127 0.036 0.032 0.021 0.031 0.090
0.013 0.028 0.021 0.078 0,035 0,061 0.024 0.031 0.035 0.045
Cure. rain
0.202 0.161 0.209 0,235 0.276 0.302 0.310 0.336 0.294 0.318
0,035 0.055 0.069 0.060 0.063 0.057 0,083 0.101 0.053 0.102
R a i n / ( t e m p . + 10)
Value o f c o e f f i c i e n t for specific climatic a t t r i b u t e s
T h e r a n k e d values of t h e C a n b e r r a m e t r i c o f the t e n m o s t similar s t a t i o n s t o K a t h e r i n e o f 349 s t a t i o n s in M e x i c o and Central A m e r i c a f o r t h e w e t season and t h e w h o l e year, w i t h respective values o f climatic a t t r i b u t e s
T A B L E IV
Country a
0.1026 0.1148 0.1273 0.1288 0.1318 0.1536 0.1568 0.1599 0.1614 0.1619
0.0747 0.0792 0.0843 0.0846 0.0858 0.0880 0.0881 0.0911 0.0917
M M M M M M H M M
M M M M M M M M M M
0.0653
G
Overall similarity c o e f f i c i e n t
a M = Mexico, G = G u a t e m a l a , H = H o n d u r a s
Linares Matamoros E n r a m a d a s Las Muzquiz Victoria Pilaresdemacozari Camargo Abasolo Piedras Negras Mendez
Whole year ( J u n e - - M a y )
Chiquimula Santiago Papasquiar Etla San J u a n Del Rio Rioverde R o d e o E1 Cerritos Yoro Tepehuanes Tlacolula
Wet season ( J u n e - - S e p t e m b e r )
Station
0.041 0.078 0.077 0.055 0.066 0.069 0.101 0.109 0.065 0.087
0.063 0.096 0.078 0.029 0.010 0.040 0.008 0.067 0.073
0.038
Temp. (°C)
9.170 0.176 0.206 0.225 0.202 0.312 0.215 0.248 0.210 0.247
0.096 0.048 0.112 0.144 0.148 0.127 0.149 0.126 0.121
0.104
Rain (mm)
0.037 0.076 0.077 0.062 0.053 0.023 0.102 0.093 0.062 0.085
0.060 0.099 0.073 0.030 0.001 0.035 0.001 0.063 0.078
0.033
Cure. temp.
0.074 0.066 0.039 0.053 0.116 0.035 0.133 0.048 0.268 0.115
0.009 0.043 0.014 0.073 0.099 0.087 0.122 0.017 0.071
0.035
Cum. rain
0.184 0.171 0.226 0.237 0.215 0.308 0.226 0.287 0.202 0.266
0.126 0.106 0.124 0.131 0.153 0.137 0.148 0.156 0.107
0.100
R a i n / ( t e m p . + 10)
Value o f c o e f f i c i e n t for specific climatic a t t r i b u t e s
The r a n k e d values o f the C a n b e r r a m e t r i c o f t h e ten m o s t similar s t a t i o n s to N a r a y e n of 349 s t a t i o n s in M e x i c o and Central A m e r i c a for the w e t season and w h o l e year w i t h respective values o f the climatic a t t r i b u t e s
TABLE V
0 4 4 4 4
0 0 0 0 5 4 0 0 0 0
P u e n t a de I x t l a Alcozauca Jonacatepec Chiautla Iguala
Chiquimula Santiago Papasquiar Etla S a n J u a n Del R i o Rioverde
Linares Matamoros E n r a m a d a s Las Muzquiz Victoria
Katherine (whole year)
Narayen (wet season)
Narayen ( w h o l e year)
12 12 12 11 12
4 4
0 0
0 0 0 1 0
12 12 12 12 7
2 2 4
2 2 0
Katherine (wet season)
3 6 3 3 6
3 3 2 1
2
5 7 6 5 8
0 2
3 3 2
+
+
--
Rain
Temperature
Huetamo Zirandaro Champoton Soledad Doblado Tela
Similar station
Reference station
9 6 9 9 6
1 1 2 3
2
7 5 6 7 4
4 2
1 1 2
--
0 0 0 0
3
0 0 0 0 5
0 0
3 3 0
11 11 11 11 11
+
3 3
0 0 3
0 0 0 0 0
3 3 3 3
0
11 11 11 11 6
--
Cumulative temperature
0 1
2 3 0
9 8 5 6 10
2 3 0 0
3
11 0 0 0 11
+
2 3 6 5 1
1 0 3 3
0
0 11 11 11 0
3 2
1 0 3
--
Cumulative rain
3 6 3 3 5
3 4 3 1
2
7 8 9 7 7
1 2
3 2 2
+
9 6 9 9 7
1 0 1 3
2
5 4 3 5 5
3 2
1 2 2
--
R a i n / ( t e m p . ÷ 10)
N u m b e r o f m o n t h s o f m o s t similar s t a t i o n s w i t h c l i m a t i c a t t r i b u t e values e q u a l to or g r e a t e r t h a n ( + ) or less t h a n (--) t h e r e f e r e n c e s t a t i o n (five m o s t similar s t a t i o n s o n l y p r e s e n t e d )
T A B L E VI
VII
Puenta de Ixtla Alcozauca Jonacatepec Chiautla Iguala
Chiquimula Santiago
Katherine (whole year)
Narayen (wet season)
Narayen (whole year)
Huetamo Zirandaro Champoton Soledad Doblado Tela
Katherine (wet season)
Linares Matamoros Enramadas Muzquiz Victoria
Las
Papasquiar Etla San Juan Del Rio Rioverde
Similar station
Reference station
0.041 0.078 0.077 0.058 0.066
-----
0.038
----0.050
0.013 0.011 ----
---0.019
0.063 0.096 0.078 0.029
--
0.046 0.112 0.093 0.059 0.019
0.003 0.003 0.021 0.017 0.039
0.300 0.187 0.204 0.269 0.222
0.062 0.058 0.079 0.245
0.176
0.276 0.173 0.231 0.191 0.207
0.041 0.049 0.057 -0.068
-I-
+
--
Rain
Temperature
Mean values of Canberra metric of most similar stations with reference station (five most similar stations only presented)
TABLE
0.126 0.166 0.206 0.210 0.182
0.197 0.017 0.146 0.110
0.033
0.155 0.138 0.179 0.268 0.387
0.036 0.070 0.082 0.067 0.068
--
climatic
-
-
-
-
-
0.037 0.076 0.077 0.062 0.053
0.033
0.007
-
-
--
-
0.009 0.007 ---
+
----
0.060 0.099 0.073 0.030
--
0.079 0.029 0.026 0.032 0.125
0.008 0.043 ---
0.035
0.035 ---0.127
0.005
0.043
0.055 0.123 0.107 0.070 0.022
0.016 0.028 ---
+
--0.024 0.015
--
0.050 0.163 0.050 0.078 0.019
0.011 -0.014 0.073
--
-0.034 0.020 0.036 --
0.050
0.005 -0.021 0.078
--
Cumulative rainfall
equal to or greater than (+)
Cumulative temperature
attributes
0.277 0.132 0.146 0.228 0.233
0.111 0.106 0.096 0.259
0.145
0.221 0.211 0.198 0.168 0.241
0.091
0.036 0.072 0.072 0.013
+
÷ 10)
0.153 0.210 0.253 0.240 0.202
0.170 -0.207 0.088
0.056
0.174 0.061 0.240 0.328 0.327
0.034
0.033 0.039 0.066 0.076
--
(Rain/(temp.
o r less t h a n ( - - ) t h e
0c ¢D
Similar station
Huetamo Zirandaro Champoton Soledad Doblado Tela
P u e n t a de I x t l a Alcozauca Jonacatepec Chiautla Iguala
Chiquimula Santiago Papasquiar Etla S a n J u a n Del R i o Rioverde
Linares Matamoros E n r a m a d a s Las Muzquiz Victoria
Reference station
Katherine (wet season)
Katherine (whole year)
Narayen (wet season)
Narayen (whole year)
-
0.077 0.103 0.097 0.085 0.103
---
--
-
0.052
----0.072
--
0.018 0.021 ---
0.019 --
--
---
0.441 0.402 0.388 0.415 0.490
0.119 0.089 0.145 0.245
0.074 0.116 0.102 0.044
0.254
0.472 0.472 0.605 0.472 0.588
--
0.075 0.143 0.127 0.084 0.032
0.003 0.003 0.027 0.027 0.049
0.097 0.087 0.078 0.000 0.115
+
+
--
Rain
Temperature
0.271 0.373 0.418 0.406 0.410
0.197 0.017 0.236 0.138
0.066
0.551 0.224 0.595 0.849 0.655
0.036 0.070 0.101 0.132 0.073
--
0 . 1 2 1
---
--
0.042
0.082 0.072 0.064
0.032
0.081
0.078 --
0.062 0.101
--
--
--
--
0.038
0.010
- -
0.082 0.029
- -
--
0.067 0.135
--0.027 0.017 0.046
--
--
0.013 0.011 ----
+
Cumulative temperature
-
0.048 0.062 0.182
0.039
0.122
--
--
0.010 0.055
0.072
-0.138
- -
-
0.041
0.020 0.053 --0.005
+
0.078 0.252 0.111 0.190 0.019
0.021 0.109
0.011
0.058 0.055 0.082
0.035 0.O85 0.068
0.005
--
Cumulative rain
0.420 0.354 0.337 0.370 0.456
0.170 0.148 0.203 0.259
0.219
0.477 0.502 0.627 0.484 0.575
0.098 0.086 0.O88 0.013 0.132
+
0.315 0.425 0.463 0.433 0.437
0.207 0.117
0.170
0.080
0.511 0.128 0.538 0.831 0.652
0.033 0.067 0.081 0.124 0.041
--
R a i n / ( t e m p . + 10)
M a x i m u m values o f C a n b e r r a m e t r i c o f m o s t s i m i l a r s t a t i o n s w i t h c l i m a t i c a t t r i b u t e s e q u a l t o o r g r e a t e r t h a n ( + ) o r less t h a n ( - - ) t h e r e f e r e n c e s t a t i o n (five m o s t s i m i l a r s t a t i o n s o n l y p r e s e n t e d )
TABLE VIII
O
F~
191 m o n t h l y t e m p e r a t u r e v a l u e s f o r H u e t a m o w e r e less t h a n K a t h e r i n e , i.e. z - - 1 was negative, the mean difference between monthly temperatures was 0.6%. Similarly for the Canberra metric values, for rainfall of 0.041 and 0.036, the mean differences were 8.6% where rainfall values were greater than K a t h e r i n e a n d 6 . 0 % w h e r e t h e y w e r e less. S i m i l a r c a l c u l a t i o n s c a n b e m a d e for Table VIII, where the maximum difference for various attributes can be c a l c u l a t e d in p e r c e n t a g e t e r m s . The numbers of Mexican and Central American stations for each reference s t a t i o n , w i t h s i m i l a r i t y c o e f f i c i e n t s less t h a n s p e c i f i e d v a l u e s f o r t h e w e t s e a s o n a n d f o r t h e w h o l e y e a r , a r e s h o w n in T a b l e I X . T h e s e d a t a s h o w t h a t there were a large number of Mexican and Central American stations with s i m i l a r i t y c o e f f i c i e n t s less t h a n 0 . 1 5 f o r t h e w e t s e a s o n o f t h e t h r e e m o s t TABLE IX Numbers of Mexican and Central American stations with similarity coefficients less than specified values in comparison with reference Australian stations Reference station
Wet season
Katherine Kimberley Research Station Charters Towers Emerald Narayen Research Station
Whole year
~0.05
~0.10
~0.15
~0.10
4
49
112
0
5
32
1 0 0
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81 96 64
0 1 3
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37 101 62
0
15
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0
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Fig. 2. Locations of 100 stations in Mexico and Central America most similar climatically to Katherine for the wet season (June--September). Symbols used; (m) is for stations ranked 1--50 and (•) is for stations ranked 51--100.
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Fig. 5. L o c a t i o n s o f 1 0 0 s t a t i o n s in M e x i c o a n d C e n t r a l A m e r i c a m o s t similar c l i m a t i c a l l y to N a r a y e n R e s e a r c h S t a t i o n for t h e w h o l e y e a r ( J u n e - - M a y ) . S y m b o l s as in Fig. 2. DISCUSSION
There is frequently a need to select homoclimates from different geographic areas using climatic data. The m e t h o d proposed makes use of the large a m o u n t of geographically extensive m o n t h l y rainfall and temperature data currently available. Large numbers of comparisons can be handled quickly and computations can also be made readily on a m o n t h l y or seasonal basis. The m e t h o d allows stations to be ranked in order of decreasing similarity. It is possible that in a set of data there are few stations showing much similarity to the reference station. However, the method does select those stations which have the lowest similarity coefficient. Also, examination of the Canberra metric values for climatic attributes enables percentage variation to be calculated in terms of values above and below the reference station. In the present analysis the Canberra metric was used as a similarity coefficient. This coefficient has an important advantage over Euclidean distance in the screening of large numbers of stations, since standardization (zero mean, unit variance) of variates involving large computer memories and greatly increased computing time is n o t necessary (Russell and Moore, 1970). Another characteristic of the Canberra metric is that it is less affected by outlying values than Euclidean distance. However, in some analyses emphasis on outlying values may be important, and, in other analyses, the data set may be small. In either situation, the use of Euclidean distance as a similarity coefficient could well be justified. One disadvantage of the Canberra metric is its inability to handle negative values (e.g. for temperature) and coding is necessary in situations where negative values occur. In the current analysis all mean temperature values were greater than 0°C.
194 It m a y also be n o t e d t h a t the C a n b e r r a m e t r i c has a singularity if X j = O. U n d e r these c o n d i t i o n s the m e t r i c t a k e s its m a x i m u m value of 1 regardless o f the value o f X k . This can be o v e r c o m e b y t r a p p i n g all z e r o / n o n - z e r o c o m p a r i s o n s a n d f o r t h a t c o m p a r i s o n o n l y replacing X j b y a small n u m b e r , usually o n e t h i r d o f the smallest n o n - z e r o value o f Xj. No a t t e m p t t o f o r m g r o u p s f r o m the r a n k e d values was m a d e in this s t u d y . Nevertheless, p r o c e d u r e s are available using s u m s o f squares, which a l l o w g r o u p s to be f o r m e d if these are required. A possible e x t e n s i o n o f the m e t h o d c o u l d be to search f o r the s t a r t o f the w e t season at each s t a t i o n before m a k i n g c o m p a r i s o n s . This avoids rigid c o m p a r i s o n s o n an e q u i v a l e n t m o n t h l y basis, as at present. In t h e c u r r e n t analysis n o weighting o f t h e climatic a t t r i b u t e s has been m a d e . It is possible t h a t e m p i r i c a l d a t a c o u l d be used to d e v e l o p a series of w e i g h t i n g factors. T h e p r o c e d u r e used is an h y p o t h e s i s - g e n e r a t i n g one. It needs f u r t h e r inf o r m a t i o n t o test the e x t e n t to which the i n d i c a t e d h o m o c l i m a t e s are, in fact, similar to the r e f e r e n c e stations. T h e a b s o l u t e value o f the similarity c o e f f i c i e n t gives s o m e i n d i c a t i o n o f this in a n y e q u i v a l e n t series o f analyses a n d t h e ratio characteristics of the C a n b e r r a m e t r i c p r o v i d e useful i n f o r m a tion. C o m p a r i s o n s o f individual and seasonal a t t r i b u t e s also enables s o m e i n d i c a t i o n o f t h e e x t e n t t o w h i c h the h o m o c l i m a t e s m a t c h the r e f e r e n c e stations. H o w e v e r , to a d e q u a t e l y test the c o m p a r i s o n s o t h e r d a t a or i n f o r m a t i o n , in a d d i t i o n to the original climatic data, are n e e d e d . T h e c o m b i n a t i o n o f this m e t h o d with the large a m o u n t o f global d a t a available in W e r n s t e d t ( 1 9 7 2 ) a n d possibly o t h e r sources, s h o u l d enable bett e r c o m p a r a t i v e i n f o r m a t i o n t o be o b t a i n e d f o r d i f f e r e n t regions of the world.
REFERENCES Clifford, H.T. and Williams, W.T., 1976. Similarity measures. In: W.T. Williams (Editor), Pattern Analysis in Agricultural Science. CSIRO, Melbourne, pp. 37--46. Gentilli, J., 1958. A Geography of Climate. University of Western Australia Press, Perth, pp. 143--147. Hutton, E.M., 1970. Australian research in plant introduction and breeding. Proc. 11th Int. Grassl. Congr., Surfers Paradise, Australia, pp. A1--A12. Russell, J.S. and Moore, A.W., 1970. Detection of homoclimates by numerical analysis with reference to the Brigalow region (Eastern Australia). Agric. Meteorol., 7: 455-479. Wernstedt, F.L., 1972. World Climatic Data. Climatic Data Press, Lemont, PA, 522 pp.
SELECTION OF HOMOCLIMATES BASED ON COMPARISONS SINGLE STATIONS AND USING MONTHLY RAINFALL AND TEMPERATURE DATA
179
WITH
J.S. RUSSELL
CSIRO, Division of Tropical Crops and Pastures, Cunningham Laboratory, St. Lucia, Qld. 4067 (Australia) (Received January 9, 1980; revision accepted December 30, 1981) ABSTRACT Russell, J.S., 1982. Selection of homoclimates based on comparisons with single stations and using monthly rainfall and temperature data. Agric. Meteorol., 26: 179--194. A method is proposed for the detection of homoclimates using the Canberra metric as a similarity coefficient to assess the large amounts of global monthly rainfall and temperature data, such as is available in Wernstedt (World Climatic Data). The method uses the dimensionless and ratio characteristics of the Canberra metric to compare stations on the basis of numerical climatic attributes. Ranking of the stations from the most similar to least similar to a reference station is carried out, enabling homoclimates to be identified. Analysis of the similarity of temperature, cumulative temperature, rainfall, cumulative rainfall and rainfall/temperature ratio attributes of homoclimates is also carried out. The method is used to compare 349 Mexican and Central American stations with five north Australian reference stations for both the wet season and the whole year. The necessity for defining homoclimates in Mexico and Central America arose from a recent plant collecting expedition to this region which had the objective of broadening the germplasm base of tropical forage legumes suitable for certain areas of northern Australia. The method maximizes the information content of the climatic data available and enables comparative climatic information for different regions of the world to be obtained quickly and cheaply. INTRODUCTION In an earlier paper, the use of pattern analysis to detect homoclimates was described (Russell and Moore, 1970). As an example, homoclimates of the Brigalow region of eastern Australia were found with 130 global stations u s i n g m o n t h l y v a l u e s o f 11 c l i m a t i c a t t r i b u t e s . There are two limitations to this approach. Firstly, the lack of detailed c h m a t i c d a t a in r e g i o n s o f t h e w o r l d w h e r e h o m o c l i m a t e s a r e l i k e l y t o b e r e q u i r e d {such as s u b t r o p i c a l a n d t r o p i c a l a r e a s ) , l i m i t s t h e a p p l i c a b i l i t y o f t h e t e c h n i q u e . S e c o n d l y , t h e c l a s s i f i c a t i o n u s e d r e s u l t s in c o m p u t i n g t i m e increasing by the square of the number of stations considered. This imposes a c o n s t r a i n t o n t h e n u m b e r o f s t a t i o n s t h a t c a n b e e v a l u a t e d in p r a c t i c e . S i n c e t h e o r i g i n a l p a p e r w a s p u b l i s h e d , s o m e p r o g r e s s h a s b e e n m a d e in the consolidation of global climatic data. In particular, the compilation of 0002-1571/82/0000--0000/$02.75
© 1982 Elsevier Scientific Publishing Company
180 m o n t h l y rainfall and temperature data for some 19,000 world stations (Wernstedt, 1972) has provided a valuable source reference. With such a large range o f stations, this source provides an extensive coverage of most countries in the world. However, its usefulness is limited by the fact that only two parameters, mean m o n t h l y rainfall and mean m o n t h l y temperature, are reported. The need to develop a more effective m e t h o d of detecting homoclimates arose as a result of a plant collecting expedition m o u n t e d in 1979 by CSIRO Division of Tropical Crops and Pastures to Mexico and Central America in c o o p e r a t i o n with national governments. This expedition had the task of collecting tropical forage legumes suitable for nort hern Australia environments. South and Central America have already been a valuable source of forage legumes genera such as Stylosanthes, Macroptilium, Desmodium and Centrosema (Hutton, 1970). These introduced legumes form the basis of improved grass--legume pastures in the nort hern Australian tropics and subtropics. The purpose of the expedition was to broaden the germplasm base of genera previously introduced and to search for legumes for specific environmerits where previous introductions have been unsuccessful, such as clay soil areas in north-eastern Australia. Mexico, Guatemala and Honduras were chosen for more intensive study because of their climatic similarity to areas o f n o r th er n Australia and because of past successful introductions from this region. Precise knowledge of similar climatic areas in the search area was thus an i m p o r t a n t planning prerequisite if the expedition was to increase its chances of successful plant collection in the limited time available, particularly as climatic gradients are very steep in parts of Mexico and Central Amercia. To assist in the definition of homoclimates, a modified m e t h o d of comparing single climatic stations was developed. This m e t h o d makes use of the geographically extensive data of Wernstedt (1972) and maximizes the information c o n t e n t of the two climatic parameters available. The m e t h o d uses a similarity coefficient to compare stations but ranking rather than grouping is used to ordinate the stations. Analysis of specific climatic attributes of the homoclimates was also carried out. METHODS
Characteristics o f the Canberra metric The similarity coefficient used was the Canberra metric which was defined by Clifford and Williams (1976) as the ratio of the absolute value of the difference between two attributes over the sum of the two attributes. For any two stations, these ratios are summed over all attributes and the mean value found, i.e.
181
1 Cjk = -- ~_ (Xij -- Xik )/(Xij + Xik ) rl
(1)
i=l
where Cjle is the similarity c o e f f i c i e n t for s t a t i o n s ] and k, Xij is the value of a t t r i b u t e i at station j and Xik is the value of a t t r i b u t e i at station k. n is the n u m b e r o f a t t r i b u t e s used in the c o m p a r i s o n . T h e Canberra metric is useful as a similarity c o e f f i c i e n t for c o m p a r i n g the numerical a t t r i b u t e s o f climatic stations because it is dimensionless and because its value is an i n d i c a t i o n o f the ratio o f the a t t r i b u t e s Xij and Xile. When n = 1 the metric can be expressed as
cj~ = I z - l l / ( z + l )
(2)
where z = X j / X k . T h e relationship b e t w e e n Cjk and z for values o f z ~> 0 is s h o w n in Fig. 1. The C a n b e r r a metric is c o n s t r a i n e d b e t w e e n 0 and 1. When Xj and Xle are equal, z = 1 and Cjle = 0. Similarity b e t w e e n the values o f the a t t r i b u t e s is thus s h o w n by low values o f the metric. There is also a relationship b e t w e e n the value o f the metric and the ratio Xj/Xle i.e. w h e n the ratio X j / X k is 2/1 or 1/2, Cjk = 0 . 3 3 3 ; w h e n the ratio is 3/1 or 1/3, Cjle = 0.5, etc. Thus the value o f the metric is an i n d i c a t i o n o f t h e ratio Xj/XIe. If Xj is greater t h a n X k , i.e. (z -- 1) is positive, t h e n the ratio of X] to X k can be calculated f r o m the value Cjk as follows
Xj/Xle = (1 + Cyk)/(1 --Cjh)
(3)
where Xj is less t h a n X k , i.e. (z -- 1) is negative, t h e n the ratio o f Xj to XIe can be calculated as follows
Xj/Xk = (1 -- Cjk)/(1 + erie)
(4)
Values of the ratio for certain values of the metric are shown in Table I. Where the metric has a value of 0.05 or less, the values of Xj and Xk do not differ by more than 10.5%. Similarly, where the metric has a value of 0.10 or ,0[ 08;
06~ j J J
i
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L_
\,
/
"\
J
/ \',
/
,~/ V a l u e of
Z
Fig. 1. Relationship between the Canberra metric and the value of z, where z is the ratio of the attributes.
182 TABLEI Values of the attribute ratio Xj/Xk for specific values of the Canberra metric, Cjk. Values of the ratio of less than 1 occur where Xj is less than Xk. Values of the ratio of more than 1 are where Xj is greater than Xk Value of Cjk
Value of the ratio X]/Xk
0.05 0.10 0.15 0.20 0.25
0.905 0.818 0.739 0.667 0.600
or or or or or
1.105 1.222 1.353 1.500 1.667
less, the values o f Xj and Xk do n o t differ by m o r e t h a n 22.2%. A t higher values o f the metric, the values o f the ratio X]/Xk b e c o m e larger b u t also b e c o m e m o r e s k e w e d percentage-wise d e p e n d i n g on w h e t h e r Xj is greater or less than Xk.
Comparisons o f stations and attributes used L o c a t i o n s o f the five stations (Katherine, K i m b e r l e y Research Station, Charters Towers, E m e r a l d and N a r a y e n Research Station) in n o r t h e r n Aust: ralia with which h o m o c l i m a t e s were sought, are s h o w n in Table II, and their m e a n m o n t h l y rainfall and t e m p e r a t u r e s are s h o w n in Table III. These stations were each c o m p a r e d with 275, 59 and 15 stations in Mexico, Guatemala and H o n d u r a s , respectively, f o r w h i c h b o t h m o n t h l y rainfall and temp e r a t u r e data were available (Wernstedt, 1972), (These d a t a are given in inches and ° F and were t r a n s f o r m e d into millimetres and °C.) As the rainfall and p l a n t g r o w t h p a t t e r n s in n o r t h e r n Australia are strongly seasonal, separate c o m p a r i s o n s for the f o u r m o n t h wet season ( D e c e m b e r - March) a n d the whole y e a r ( D e c e m b e r - - N o v e m b e r ) were made. Equivalent m o n t h s in the n o r t h e r n h e m i s p h e r e are J u n e - - S e p t e m b e r , and J u n e - - M a y . In a d d i t i o n t o the individual m o n t h l y values o f rainfall, a series o f cumula-
TABLE II Locations of the five reference stations for which homoclimates in Mexico and Central America were sought Station
Latitude (°S)
Longitude (°E)
Altitude (m)
Katherine Kimberley Research Station Charters Towers Emerald Narayen Research Station
14 ° 15 ° 20 ° 23 ° 25 °
132 ° 128 ° 146 ° 148 ° 150 °
108 37 306 175 280
28'S 30'S 4'S 32'S 41'S
18'E 43' E 16'E 10'E 52'E
219
200 132 100
96
190 139 108
107
Katherine Kimberley Research Station Charters T o w e r s Emerald N a r a y e n Research Station
Feb.
201
Jan.
28.8
29.6 27.2 27.1
24.7
29.2
30.2 27.6 27.4
25.4
Mean m o n t h l y t e m p e r a t u r e
Katherine Kimberley Research Station Charters T o w e r s Emerald Narayen R e s e a r c h Station
Rainfall
Station
23.6
29.4 25.8 25.5
28.4
73
116 104 72
164
Mar.
20.5
27.8 23.7 22.8
26.7
37
47 38 34
48
Apr.
16.9
25.2 20.8 18.6
24.0
39
12 20 27
5
May
13.9
22.8 18.2 15.8
21.4
37
3 28 36
2
June
M o n t h l y rainfall ( m m ) a n d m e a n t e m p e r a t u r e (°C) for t h e r e f e r e n c e s t a t i o n s
T A B L E III
13.2
22.2 17.4 14.5
21.1
36
6 16 27
2
July
14.8
24.0 19.6 16.6
23.2
27
1 12 22
1
Aug.
17.3
27.4 22.0 20.0
26.9
34
3 16 24
6
Sept.
21.2
30.6 25.1 24.0
30.5
55
22 19 38
28
Oct.
23.7
31.2 27.1 26.4
31.0
77
62 41 57
79
Nov.
25.2
31.2 27.7 27.2
30.1
101
126 85 86
155
Dec.
20.1
27.7 23.5 22.2
26.8
719
788 650 631
910
G¢ ¢,o
Annual total
184 tive m o n t h l y rainfall and t e m per a t ur e values were calculated for each analysis at each station. The possibility of using empirical t em perat ure relations to estimate m o n t h l y evaporation, and hence m o n t h l y rainfall/evaporation ratios, was considered. However, there can be large errors in estimating evaporation and it was decided to use the simple De Martonne index R / ( T + 10) instead (Gentilli, 1958) where R is rainfall and T is temperature. Thus the mean m o n t h l y value of rainfall (in mm) divided by mean m o n t h l y temperature (°C + 10) was calculated. This index does not p u r p o r t to measure evaporation b u t is a useful indication of the relative m o n t h l y balance on rainfall and evaporation. In all, each station was represented by 18 attributes in the case o f the wet season analysis, and 58 attributes in the case of the whole year analysis. (The 18 attributes comprised 4 m o n t h l y values of rainfall, temperature and de Martonne index respectively, plus 3 values of cumulative rainfall and tem pe r at ur e respectively. The 58 attributes comprised 12 m o n t h l y values o f rainfall etc.)
Application o f the method and assessment of homoclimates Each Australian station was compared with the 349 Mexican and Central American stations for both summer and the whole year over the 18 or 58 attributes respectively, using the Canberra metric. In each analysis the 349 similarity coefficients were then ranked in increasing value. The station with the lowest value had the closest match to the Australian station based on the available data and the m e t h o d used. In addition to calculating an overall value of the Canberra metric, further analyses were carried out to determine the cont ri but i on of the various climatic attributes to the mean value. The following additional information was obtained for each station: (1) Canberra metrics for each station and the reference station were calculated for each climatic attribute over the months considered. Thus, in addition to a single similarity coefficient, values for temperature, cumulative temperature, rainfall, cumulative rainfall and the rainfall/temperature ratio were calculated. The sum of these, weighted in each case for the months over which th ey were calculated, gives the overall Canberra metric used for ranking. (2) The n u m b e r of m ont hs in each comparison where Xj was equal to or greater than X k or less than X k was recorded for each climatic attribute over the m o n t h s considered. This indicated how m any m ont hs had higher or lower temperature, rainfall, etc. than the reference station. {3) Canberra metrics were calculated separately for climatic attributes over all mo n th s considered where Xj was equal to or greater than Xk and where Xj was less than Xk. Fr om the means of these values it was possible to calculate the mean percentage difference of the climatic attribute from the reference site. (4) Maximum values of the Canberra metric were calculated separately for
185
climatic a t t r i b u t e s o v e r all m o n t h s c o n s i d e r e d , w h e r e X] was equal to or greater t h a n Xk a n d w h e r e X] was less t h a n Xk. This allowed the p e r c e n t a g e d i f f e r e n c e o f the m o s t d e v i a n t m o n t h for the climatic a t t r i b u t e to be calculated. This a d d i t i o n a l i n f o r m a t i o n e n a b l e d assessments to be m a d e o f similarities o f the various climatic a t t r i b u t e s of the h o m o c l i m a t e s with the r e f e r e n c e stations. RESULTS A l t h o u g h calculations were carried o u t for all stations, detailed c o m p a r i sons with the ten m o s t similar Mexican and Central A m e r i c a n s t a t i o n s are p r e s e n t e d f o r K a t h e r i n e and the N a r a y e n R e s e a r c h S t a t i o n only. C o m p a r i sons f o r the w e t season and the w h o l e y e a r a n d b o t h the overall similarity c o e f f i c i e n t a n d t h e similarity c o e f f i c i e n t s for specific climatic a t t r i b u t e s are s h o w n in T a b l e s IV and V. T h e analysis s h o w e d n o t o n l y the m o s t similar s t a t i o n s b u t also the relative c o n t r i b u t i o n o f the various climatic a t t r i b u t e s t o the overall similarity c o e f f i c i e n t . In s o m e cases the m o s t similar s t a t i o n was m o s t similar in all a t t r i b u t e s . H o w e v e r , in m a n y cases this was n o t the case. T h u s in the w h o l e y e a r analysis in T a b l e IV, t h e stations Iguala, H u e t a m o a n d Salina Cruz had m o r e similar t e m p e r a t u r e p a t t e r n s t o K a t h e r i n e t h a n P u e n t a de I x t l a b u t this was o f f s e t b y m o r e dissimilar rainfall p a t t e r n s . Likewise, Etla (Table V ) h a d a m o r e similar rainfall p a t t e r n t o N a r a y e n t h a n C h i q u i m u l a b u t this was o f f s e t b y a less similar t e m p e r a t u r e p a t t e r n . A m o r e d e t a i l e d analysis of the climatic a t t r i b u t e s o f the five m o s t similar s t a t i o n s is s h o w n in T a b l e s VI, V I I and V I I I . T a b l e VI indicates the n u m b e r o f m o n t h l y values o f the climatic a t t r i b u t e s equal t o or greater t h a n the r e f e r e n c e s t a t i o n a n d values less t h a n the r e f e r e n c e station. This allows c o m p a r i s o n s o f s t a t i o n s in t e r m s o f w h e t h e r , f o r e x a m p l e , t e m p e r a t u r e or rainfall are c o n s i s t e n t l y a b o v e or b e l o w t h e values f o r the r e f e r e n c e station. T a b l e V I I s h o w s t h e m e a n C a n b e r r a m e t r i c values o f a t t r i b u t e values equal t o o r a b o v e t h e r e f e r e n c e s t a t i o n and t h o s e b e l o w the r e f e r e n c e station. This enables an e s t i m a t e o f the m e a n p e r c e n t a g e v a r i a t i o n o f the a t t r i b u t e c o m p a r e d with the r e f e r e n c e station. T a b l e V I I I indicates the m a x i m u m Canb e r r a m e t r i c f o r the a t t r i b u t e values equal to or a b o v e the r e f e r e n c e s t a t i o n a n d t h o s e b e l o w the r e f e r e n c e station. This enables the p e r c e n t a g e v a r i a t i o n o f t h e m o s t d e v i a n t a t t r i b u t e c o m p a r e d with r e f e r e n c e s t a t i o n t o be determined. T h e d a t a in T a b l e V I I can be used f o r c o n v e r t i n g b a c k t o the relative values o f t h e original a t t r i b u t e s . T h u s f o r H u e t a m o , the C a n b e r r a m e t r i c values f o r t e m p e r a t u r e in c o m p a r i s o n w i t h K a t h e r i n e were 0 . 0 1 3 w h e r e the ratio Xj/Xk was equal to or greater t h a n 1 and 0 . 0 0 3 w h e r e Xj/Xk was less t h a n 1. Using eqs. 3 a n d 4 it can be c a l c u l a t e d t h a t w h e r e m o n t h l y t e m p e r a ture values f o r H u e t a m o were greater t h a n K a t h e r i n e , i.e. (z -- 1) was positire, t h e m e a n d i f f e r e n c e b e t w e e n m o n t h l y t e m p e r a t u r e s was 2.6% Where
Country a
M M M M M G M M M M
M M M M H M M M M M
0.1107 0.1191 0.1290 0.1296 0.1460 0.1537 0.1546 0.1549 0.1559 0.1599
0.0219 0.0318 0.0430 0.0475 0.0507 0.0517 0.0536 0.0548 0.0548 0.0606
Overall similarity c o e f f i c i e n t
a M = Mexico, G = G u a t e m a l a , H = H o n d u r a s
P u e n t e de Ixtla Alcozauca Jonacatepec Chiautla Iguala Amatitlan T u x t l a Gutierrez Huetamo Cintalapa Salina Cruz
Whole year ( J u n e - - M a y )
Huetamo Zirandaro Champoton Soledad Doblado Tela Campeche C a r m e n Ciudad G u e r r e r o Villa Colima Rio M a n t e
Wet season ( J u n e - - S e p t e m b e r )
Station
0.046 0,112 0.093 0.059 0.032 0,056 0,046 0.033 0.068 0.041
0.008 0.007 0,021 0.017 0.039 0.034 0.032 0.016 0.061 0.026
Temp. (°C)
0.205 0.158 0.205 0.236 0,267 0,301 0.312 0.341 0.295 0.316
0.040 0.054 0,070 0.067 0.068 0.067 0.081 0,092 0.060 0,090
Rain (mm)
0.055 0.123 0.107 0.070 0.015 0,056 0,055 0.020 0,075 0.016
0.009 0.007 0.024 0,015 0,043 0,039 0.036 0.019 0.062 0.027
Cum. temp.
0.035 0.034 0.020 0,036 0,127 0.036 0.032 0.021 0.031 0.090
0.013 0.028 0.021 0.078 0,035 0,061 0.024 0.031 0.035 0.045
Cure. rain
0.202 0.161 0.209 0,235 0.276 0.302 0.310 0.336 0.294 0.318
0,035 0.055 0.069 0.060 0.063 0.057 0,083 0.101 0.053 0.102
R a i n / ( t e m p . + 10)
Value o f c o e f f i c i e n t for specific climatic a t t r i b u t e s
T h e r a n k e d values of t h e C a n b e r r a m e t r i c o f the t e n m o s t similar s t a t i o n s t o K a t h e r i n e o f 349 s t a t i o n s in M e x i c o and Central A m e r i c a f o r t h e w e t season and t h e w h o l e year, w i t h respective values o f climatic a t t r i b u t e s
T A B L E IV
Country a
0.1026 0.1148 0.1273 0.1288 0.1318 0.1536 0.1568 0.1599 0.1614 0.1619
0.0747 0.0792 0.0843 0.0846 0.0858 0.0880 0.0881 0.0911 0.0917
M M M M M M H M M
M M M M M M M M M M
0.0653
G
Overall similarity c o e f f i c i e n t
a M = Mexico, G = G u a t e m a l a , H = H o n d u r a s
Linares Matamoros E n r a m a d a s Las Muzquiz Victoria Pilaresdemacozari Camargo Abasolo Piedras Negras Mendez
Whole year ( J u n e - - M a y )
Chiquimula Santiago Papasquiar Etla San J u a n Del Rio Rioverde R o d e o E1 Cerritos Yoro Tepehuanes Tlacolula
Wet season ( J u n e - - S e p t e m b e r )
Station
0.041 0.078 0.077 0.055 0.066 0.069 0.101 0.109 0.065 0.087
0.063 0.096 0.078 0.029 0.010 0.040 0.008 0.067 0.073
0.038
Temp. (°C)
9.170 0.176 0.206 0.225 0.202 0.312 0.215 0.248 0.210 0.247
0.096 0.048 0.112 0.144 0.148 0.127 0.149 0.126 0.121
0.104
Rain (mm)
0.037 0.076 0.077 0.062 0.053 0.023 0.102 0.093 0.062 0.085
0.060 0.099 0.073 0.030 0.001 0.035 0.001 0.063 0.078
0.033
Cure. temp.
0.074 0.066 0.039 0.053 0.116 0.035 0.133 0.048 0.268 0.115
0.009 0.043 0.014 0.073 0.099 0.087 0.122 0.017 0.071
0.035
Cum. rain
0.184 0.171 0.226 0.237 0.215 0.308 0.226 0.287 0.202 0.266
0.126 0.106 0.124 0.131 0.153 0.137 0.148 0.156 0.107
0.100
R a i n / ( t e m p . + 10)
Value o f c o e f f i c i e n t for specific climatic a t t r i b u t e s
The r a n k e d values o f the C a n b e r r a m e t r i c o f t h e ten m o s t similar s t a t i o n s to N a r a y e n of 349 s t a t i o n s in M e x i c o and Central A m e r i c a for the w e t season and w h o l e year w i t h respective values o f the climatic a t t r i b u t e s
TABLE V
0 4 4 4 4
0 0 0 0 5 4 0 0 0 0
P u e n t a de I x t l a Alcozauca Jonacatepec Chiautla Iguala
Chiquimula Santiago Papasquiar Etla S a n J u a n Del R i o Rioverde
Linares Matamoros E n r a m a d a s Las Muzquiz Victoria
Katherine (whole year)
Narayen (wet season)
Narayen ( w h o l e year)
12 12 12 11 12
4 4
0 0
0 0 0 1 0
12 12 12 12 7
2 2 4
2 2 0
Katherine (wet season)
3 6 3 3 6
3 3 2 1
2
5 7 6 5 8
0 2
3 3 2
+
+
--
Rain
Temperature
Huetamo Zirandaro Champoton Soledad Doblado Tela
Similar station
Reference station
9 6 9 9 6
1 1 2 3
2
7 5 6 7 4
4 2
1 1 2
--
0 0 0 0
3
0 0 0 0 5
0 0
3 3 0
11 11 11 11 11
+
3 3
0 0 3
0 0 0 0 0
3 3 3 3
0
11 11 11 11 6
--
Cumulative temperature
0 1
2 3 0
9 8 5 6 10
2 3 0 0
3
11 0 0 0 11
+
2 3 6 5 1
1 0 3 3
0
0 11 11 11 0
3 2
1 0 3
--
Cumulative rain
3 6 3 3 5
3 4 3 1
2
7 8 9 7 7
1 2
3 2 2
+
9 6 9 9 7
1 0 1 3
2
5 4 3 5 5
3 2
1 2 2
--
R a i n / ( t e m p . ÷ 10)
N u m b e r o f m o n t h s o f m o s t similar s t a t i o n s w i t h c l i m a t i c a t t r i b u t e values e q u a l to or g r e a t e r t h a n ( + ) or less t h a n (--) t h e r e f e r e n c e s t a t i o n (five m o s t similar s t a t i o n s o n l y p r e s e n t e d )
T A B L E VI
VII
Puenta de Ixtla Alcozauca Jonacatepec Chiautla Iguala
Chiquimula Santiago
Katherine (whole year)
Narayen (wet season)
Narayen (whole year)
Huetamo Zirandaro Champoton Soledad Doblado Tela
Katherine (wet season)
Linares Matamoros Enramadas Muzquiz Victoria
Las
Papasquiar Etla San Juan Del Rio Rioverde
Similar station
Reference station
0.041 0.078 0.077 0.058 0.066
-----
0.038
----0.050
0.013 0.011 ----
---0.019
0.063 0.096 0.078 0.029
--
0.046 0.112 0.093 0.059 0.019
0.003 0.003 0.021 0.017 0.039
0.300 0.187 0.204 0.269 0.222
0.062 0.058 0.079 0.245
0.176
0.276 0.173 0.231 0.191 0.207
0.041 0.049 0.057 -0.068
-I-
+
--
Rain
Temperature
Mean values of Canberra metric of most similar stations with reference station (five most similar stations only presented)
TABLE
0.126 0.166 0.206 0.210 0.182
0.197 0.017 0.146 0.110
0.033
0.155 0.138 0.179 0.268 0.387
0.036 0.070 0.082 0.067 0.068
--
climatic
-
-
-
-
-
0.037 0.076 0.077 0.062 0.053
0.033
0.007
-
-
--
-
0.009 0.007 ---
+
----
0.060 0.099 0.073 0.030
--
0.079 0.029 0.026 0.032 0.125
0.008 0.043 ---
0.035
0.035 ---0.127
0.005
0.043
0.055 0.123 0.107 0.070 0.022
0.016 0.028 ---
+
--0.024 0.015
--
0.050 0.163 0.050 0.078 0.019
0.011 -0.014 0.073
--
-0.034 0.020 0.036 --
0.050
0.005 -0.021 0.078
--
Cumulative rainfall
equal to or greater than (+)
Cumulative temperature
attributes
0.277 0.132 0.146 0.228 0.233
0.111 0.106 0.096 0.259
0.145
0.221 0.211 0.198 0.168 0.241
0.091
0.036 0.072 0.072 0.013
+
÷ 10)
0.153 0.210 0.253 0.240 0.202
0.170 -0.207 0.088
0.056
0.174 0.061 0.240 0.328 0.327
0.034
0.033 0.039 0.066 0.076
--
(Rain/(temp.
o r less t h a n ( - - ) t h e
0c ¢D
Similar station
Huetamo Zirandaro Champoton Soledad Doblado Tela
P u e n t a de I x t l a Alcozauca Jonacatepec Chiautla Iguala
Chiquimula Santiago Papasquiar Etla S a n J u a n Del R i o Rioverde
Linares Matamoros E n r a m a d a s Las Muzquiz Victoria
Reference station
Katherine (wet season)
Katherine (whole year)
Narayen (wet season)
Narayen (whole year)
-
0.077 0.103 0.097 0.085 0.103
---
--
-
0.052
----0.072
--
0.018 0.021 ---
0.019 --
--
---
0.441 0.402 0.388 0.415 0.490
0.119 0.089 0.145 0.245
0.074 0.116 0.102 0.044
0.254
0.472 0.472 0.605 0.472 0.588
--
0.075 0.143 0.127 0.084 0.032
0.003 0.003 0.027 0.027 0.049
0.097 0.087 0.078 0.000 0.115
+
+
--
Rain
Temperature
0.271 0.373 0.418 0.406 0.410
0.197 0.017 0.236 0.138
0.066
0.551 0.224 0.595 0.849 0.655
0.036 0.070 0.101 0.132 0.073
--
0 . 1 2 1
---
--
0.042
0.082 0.072 0.064
0.032
0.081
0.078 --
0.062 0.101
--
--
--
--
0.038
0.010
- -
0.082 0.029
- -
--
0.067 0.135
--0.027 0.017 0.046
--
--
0.013 0.011 ----
+
Cumulative temperature
-
0.048 0.062 0.182
0.039
0.122
--
--
0.010 0.055
0.072
-0.138
- -
-
0.041
0.020 0.053 --0.005
+
0.078 0.252 0.111 0.190 0.019
0.021 0.109
0.011
0.058 0.055 0.082
0.035 0.O85 0.068
0.005
--
Cumulative rain
0.420 0.354 0.337 0.370 0.456
0.170 0.148 0.203 0.259
0.219
0.477 0.502 0.627 0.484 0.575
0.098 0.086 0.O88 0.013 0.132
+
0.315 0.425 0.463 0.433 0.437
0.207 0.117
0.170
0.080
0.511 0.128 0.538 0.831 0.652
0.033 0.067 0.081 0.124 0.041
--
R a i n / ( t e m p . + 10)
M a x i m u m values o f C a n b e r r a m e t r i c o f m o s t s i m i l a r s t a t i o n s w i t h c l i m a t i c a t t r i b u t e s e q u a l t o o r g r e a t e r t h a n ( + ) o r less t h a n ( - - ) t h e r e f e r e n c e s t a t i o n (five m o s t s i m i l a r s t a t i o n s o n l y p r e s e n t e d )
TABLE VIII
O
F~
191 m o n t h l y t e m p e r a t u r e v a l u e s f o r H u e t a m o w e r e less t h a n K a t h e r i n e , i.e. z - - 1 was negative, the mean difference between monthly temperatures was 0.6%. Similarly for the Canberra metric values, for rainfall of 0.041 and 0.036, the mean differences were 8.6% where rainfall values were greater than K a t h e r i n e a n d 6 . 0 % w h e r e t h e y w e r e less. S i m i l a r c a l c u l a t i o n s c a n b e m a d e for Table VIII, where the maximum difference for various attributes can be c a l c u l a t e d in p e r c e n t a g e t e r m s . The numbers of Mexican and Central American stations for each reference s t a t i o n , w i t h s i m i l a r i t y c o e f f i c i e n t s less t h a n s p e c i f i e d v a l u e s f o r t h e w e t s e a s o n a n d f o r t h e w h o l e y e a r , a r e s h o w n in T a b l e I X . T h e s e d a t a s h o w t h a t there were a large number of Mexican and Central American stations with s i m i l a r i t y c o e f f i c i e n t s less t h a n 0 . 1 5 f o r t h e w e t s e a s o n o f t h e t h r e e m o s t TABLE IX Numbers of Mexican and Central American stations with similarity coefficients less than specified values in comparison with reference Australian stations Reference station
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Fig. 5. L o c a t i o n s o f 1 0 0 s t a t i o n s in M e x i c o a n d C e n t r a l A m e r i c a m o s t similar c l i m a t i c a l l y to N a r a y e n R e s e a r c h S t a t i o n for t h e w h o l e y e a r ( J u n e - - M a y ) . S y m b o l s as in Fig. 2. DISCUSSION
There is frequently a need to select homoclimates from different geographic areas using climatic data. The m e t h o d proposed makes use of the large a m o u n t of geographically extensive m o n t h l y rainfall and temperature data currently available. Large numbers of comparisons can be handled quickly and computations can also be made readily on a m o n t h l y or seasonal basis. The m e t h o d allows stations to be ranked in order of decreasing similarity. It is possible that in a set of data there are few stations showing much similarity to the reference station. However, the method does select those stations which have the lowest similarity coefficient. Also, examination of the Canberra metric values for climatic attributes enables percentage variation to be calculated in terms of values above and below the reference station. In the present analysis the Canberra metric was used as a similarity coefficient. This coefficient has an important advantage over Euclidean distance in the screening of large numbers of stations, since standardization (zero mean, unit variance) of variates involving large computer memories and greatly increased computing time is n o t necessary (Russell and Moore, 1970). Another characteristic of the Canberra metric is that it is less affected by outlying values than Euclidean distance. However, in some analyses emphasis on outlying values may be important, and, in other analyses, the data set may be small. In either situation, the use of Euclidean distance as a similarity coefficient could well be justified. One disadvantage of the Canberra metric is its inability to handle negative values (e.g. for temperature) and coding is necessary in situations where negative values occur. In the current analysis all mean temperature values were greater than 0°C.
194 It m a y also be n o t e d t h a t the C a n b e r r a m e t r i c has a singularity if X j = O. U n d e r these c o n d i t i o n s the m e t r i c t a k e s its m a x i m u m value of 1 regardless o f the value o f X k . This can be o v e r c o m e b y t r a p p i n g all z e r o / n o n - z e r o c o m p a r i s o n s a n d f o r t h a t c o m p a r i s o n o n l y replacing X j b y a small n u m b e r , usually o n e t h i r d o f the smallest n o n - z e r o value o f Xj. No a t t e m p t t o f o r m g r o u p s f r o m the r a n k e d values was m a d e in this s t u d y . Nevertheless, p r o c e d u r e s are available using s u m s o f squares, which a l l o w g r o u p s to be f o r m e d if these are required. A possible e x t e n s i o n o f the m e t h o d c o u l d be to search f o r the s t a r t o f the w e t season at each s t a t i o n before m a k i n g c o m p a r i s o n s . This avoids rigid c o m p a r i s o n s o n an e q u i v a l e n t m o n t h l y basis, as at present. In t h e c u r r e n t analysis n o weighting o f t h e climatic a t t r i b u t e s has been m a d e . It is possible t h a t e m p i r i c a l d a t a c o u l d be used to d e v e l o p a series of w e i g h t i n g factors. T h e p r o c e d u r e used is an h y p o t h e s i s - g e n e r a t i n g one. It needs f u r t h e r inf o r m a t i o n t o test the e x t e n t to which the i n d i c a t e d h o m o c l i m a t e s are, in fact, similar to the r e f e r e n c e stations. T h e a b s o l u t e value o f the similarity c o e f f i c i e n t gives s o m e i n d i c a t i o n o f this in a n y e q u i v a l e n t series o f analyses a n d t h e ratio characteristics of the C a n b e r r a m e t r i c p r o v i d e useful i n f o r m a tion. C o m p a r i s o n s o f individual and seasonal a t t r i b u t e s also enables s o m e i n d i c a t i o n o f t h e e x t e n t t o w h i c h the h o m o c l i m a t e s m a t c h the r e f e r e n c e stations. H o w e v e r , to a d e q u a t e l y test the c o m p a r i s o n s o t h e r d a t a or i n f o r m a t i o n , in a d d i t i o n to the original climatic data, are n e e d e d . T h e c o m b i n a t i o n o f this m e t h o d with the large a m o u n t o f global d a t a available in W e r n s t e d t ( 1 9 7 2 ) a n d possibly o t h e r sources, s h o u l d enable bett e r c o m p a r a t i v e i n f o r m a t i o n t o be o b t a i n e d f o r d i f f e r e n t regions of the world.
REFERENCES Clifford, H.T. and Williams, W.T., 1976. Similarity measures. In: W.T. Williams (Editor), Pattern Analysis in Agricultural Science. CSIRO, Melbourne, pp. 37--46. Gentilli, J., 1958. A Geography of Climate. University of Western Australia Press, Perth, pp. 143--147. Hutton, E.M., 1970. Australian research in plant introduction and breeding. Proc. 11th Int. Grassl. Congr., Surfers Paradise, Australia, pp. A1--A12. Russell, J.S. and Moore, A.W., 1970. Detection of homoclimates by numerical analysis with reference to the Brigalow region (Eastern Australia). Agric. Meteorol., 7: 455-479. Wernstedt, F.L., 1972. World Climatic Data. Climatic Data Press, Lemont, PA, 522 pp.