Paddy Water Environ (2012) 10:31–39 DOI 10.1007/s10333-011-0258-2
ARTICLE
A spatial aggregation index for effective fallow decision in paddy irrigation demand planning Ming-Daw Su • Mei-Chun Lin • Chun-Hung Lin Shih-Fu Wang • Tzai-Hung Wen • Hsin-I Hsieh
•
Received: 23 September 2010 / Revised: 19 December 2010 / Accepted: 20 January 2011 / Published online: 3 February 2011 Ó Springer-Verlag 2011
Abstract As irrigation demands usually take the largest share of water supply, paddy fallow is considered as a drought relieving measure in some Asian paddy growing countries by transferring the water saved to the municipal and industrial sectors. But the relationship between fallow area and irrigation demand reduction is not necessarily linear, there may be more than dozens combinations of fallow farm that can meet the same amount of irrigation demand reduction requirement. The Joint Count Statistics (JCS), an index commonly used in spatial analysis to measure the spatial coherence among cells was modified as a spatial aggregation index for evaluating the irrigation demand reduction effectiveness from a spatial perspective. This Modified JCS is supposed to identify the degree of spatial aggregation by taking underlying irrigation network into considerations. The modified JCS was proved to be effective to identify better fallow pattern through a case study in Taiwan. Keywords Join count statistics Spatial analysis Aggregation Irrigation Fallow
M.-D. Su M.-C. Lin C.-H. Lin (&) H.-I. Hsieh Department of Bioenvironmental Systems Engineering, National Taiwan University, Taipei, Taiwan e-mail:
[email protected] S.-F. Wang CECI Engineering Consultants Inc., Taipei, Taiwan T.-H. Wen Department of Geography, National Taiwan University, Taipei, Taiwan
Introduction Like most paddy growing countries in Asia, Taiwan suffers from water deficit due to population growth and rapid industrial development. Agricultural water use sector usually consumes a large portion of water supplies and Paddy fallow becomes a temperately drought mitigation measure. The water saved from the irrigation demands of the fallow paddy fields is then transferred to municipal and industrial sectors to alleviate the economical impacts. Two spatial parameters, the fallow location (where) and extent (how much), need to be decided during this drought mitigation operation. Although larger fallow area may reduce more irrigation demand, the relationship between fallow area and irrigation demand reduction is not necessarily linearly proportional (Wang 2006). Many fallow farm arrangements (in terms of area size and location) may meet the same required amount of irrigation demand reduction. There are many factors other than area involved, such as those of soil, cropping pattern, and the length and maintenance condition of the conveyance canals. If the fallow areas are more distant from the water supply sources or the delivery canals are poorly maintained, more irrigation demand reduction can be achieved from fallow due to the higher conveyance loss in these areas. Since most of these factors are spatially distributed, the location and distribution pattern of fallow farms should be more carefully considered. The spatial patterns of the fallow farms may also affect the amount of irrigation reduction from this fallow action. If the fallow farms are spatially scattered, the irrigation reduction will be much smaller than when they are more aggregated and compact in spatial sense. More water is needed to irrigate the spatially scattered farms due to its higher conveyance losses and more difficult farm irrigation management (Tsai 1996). The effectiveness of
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Fig. 1 Typical framework of an irrigation network
irrigation demand reduction of a fallow decision may be highly influenced by the spatial pattern of the fallow areas (Tsai 1996; Lee et al. 2005; Wang 2006; Wen et al. 2004). Inappropriate decision may lead to larger fallow area than actually necessary and cause higher societal and economical impacts to the farmer community as well as low efficiency in regional water use (Lin 1993; Tsai 1996; Lee et al. 2005). Although optimization models can be used to solve this complicated problem (Moghaddasi et al. 2010), the solution may not be adaptive in realistic management and operation situations due to some other (political or managerial) concerns that cannot be easily included in the objective function. A compromised solution may be more acceptable than the optimal one in a realistic situation especially there are many stakeholders involved. The final solution is usually a result of the negotiation process (Wen et al. 2007). Evaluation indices are needed for effectiveness comparison among different fallow decision scenarios for better fallow decisions. A spatial aggregation index was proposed in this article for fallow scenario evaluations in irrigation demand planning.
reservoir and delivered to the fields through a hierarchical irrigation network. As shown in Fig. 1, the conveyance network system consists of main canals, sub-main canals, laterals, and tertiary ditches (not shown). As previously discussed, the goal is to choose the fallow areas as aggregated and as close to each other as possible to save most irrigation demand from the fallowed areas. But the traditional definition or recognition of neighborhood may lead to error conclusions for some spatial objects whose spatial relationships are formed by specific underlined characteristics. Some examples are areas linked by transportation routes, or farms irrigated by irrigation network. Two bordering areas may not be connected by road network, and adjacent fields may be irrigated by canals from different water sources. Two irrigated areas that are spatially close to each other may receive their water from different supply sources. Take two farms show in Fig. 1 as an example; although the area ‘‘a’’ is neighbor to area ‘‘b’’, it is irrigated by water from the reservoir instead of the water diverted from the river. This special property of irrigated farms needs to be properly considered when the spatial aggregation characteristic of fallow farms is to be examined.
Irrigation systems The irrigation management in Taiwan is featured with its large command area and centralized water supplies. Farms are usually small (mostly less than one hectare) and the irrigation management is carried out collectively by irrigation association (IA). Water is diverted from river or
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Join count statistics The Join count statistics (JCS) is one of the simplest measures for spatial autocorrelation studies (Cliff and Ord 1973). The JCS was originally developed to examine the
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spatial autocorrelation among areas with binary characteristics of 0/1 or BW (Black and White). The JCS is designated for a binary variable (1 or 0). A binary count, referred to as Black (B) or White (W), is assigned for each cell showing its status, e.g., developed or undeveloped, cultivated or uncultivated, etc. The join of two cells/grids/ polygons, i.e., the sharing border, is classified as B/B (or 1/1), B/W (or 1/0), or W/W (or 0/0) according to the two neighbor cells. The neighborhood is usually defined as sharing common borders/vertices according to Rook’s or Queen’s rule (De Smith et al. 2006). The JCS is defined as Eq. 1. The JCS is a spatially weighted count of the BB, BW, and WW join numbers in the study area. This observed JCS is then compared to the expected numbers of BB, BW, and WW joins under the null hypothesis of no spatial autocorrelation (Wong and Lee 2005). 1X X JCS ¼ ðWij Xi Xj Þ ð1Þ i j 2 where Xi and Xj are binary counts showing the cells’ status (B/W or 0/1); Wij is the spatial weighting factor showing the connectivity between two cells of Xi and Xj. Wij = 1 if Xi and Xj is spatially connected to each other according to either Rook’s or Queen’s rule, otherwise Wij = 0. The calculated JCS for a specific pattern will then be compared with a pattern of complete spatially random (CSR) one. If the observed JCS is not statistically significantly different from the one of CSR, then we cannot reject the null hypothesis that the pattern is spatially random distributed. Otherwise, we may conclude that the pattern is either clustered or dispersed. JCS was developed for processing binary data, but nominal or ordinal data can be transformed into binary with some cutoff threshold. It has been noticed that the JCS is sensitive to grid cell resolution and the shape and arrangement of the lattices (De Smith et al. 2006). Although not commonly implemented in mainstream GIS packages, JCS is a useful tool for detecting clusters with binary data. JCS is used to measure the spatial coherence among cells or pixels. The applications of JCS in spatial analysis can be found in biology (Bonnot et al. 2010; Hui 2009; Bosiacka et al. 2008; Chung et al. 2006; Dejong and Debree 1995; Jarvinen 1989), ecology (Franklin et al. 2009; Corbane et al. 2008; Bucci and Menozzi 2002; Dube et al. 2001), disease and epidemiology (Bell et al. 2008; Muir et al. 2004; Meng et al. 2005; Mannelli et al. 1998; Hungerford 1991), image processing (Chuang and Huang 1992a, b), as well as manufacturing management electronics (Jeong et al. 2008; Fellows et al. 2009). As discussed above, the irrigation demand reduction from the fallow paddy will be varied according to the spatial pattern of the fallow areas. The aggregated fallow pattern may result with higher irrigation demand reduction and easier irrigation management comparing to scattered
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one because some canals may be completely shut off. While a scattered fallow pattern may need more canals to be operated because some farms irrigated by the same canal may still under cultivation. The JCS has been proposed for identifying the degree of spatial aggregation for paddy rice fallow decision in a water resource reallocation process for drought mitigation (Chen et al. 2008). The JCS can be used to indicate the degree of clustering of the fallow fields. The index is higher when most of the fallow fields are adjacent to each other. Water saved from the fallow paddy fields are transferred to lower down the water deficit in residential, industrial, or commercial water use sectors. There are three fallow patterns shown in Fig. 2a–c. If x = 1 is assigned to fallow fields and x = 0 is assigned to the cultivated fields, the JCS are calculated using Eq. 1 to be 45, 45, and 32 for patterns shown in Fig. 2d–f, respectively. It is clearly that fallow patterns of Fig. 2a, b are more spatially aggregated than that of Fig. 2c The numbers shown in the cells at the lower part of Fig. 2 show the computations of Ri Rj Wij Xi Xj for each fallow patterns. The Queen’s rule was applied here for adjacency identification. For general spatial data, the patterns shown in Fig. 2a, b have the same degree of adjacency or aggregation with same JCSs of 45. But it has been noticed that the definition of spatial closeness for the irrigated farms may be different from the regular grid system used in the traditional JCS studies. The adjacency characteristics of irrigated fields are different from ordinary spatial data because the water is delivered to the fields through the irrigation canal network. Two farms physically next to each other may be irrigated by different canals as shown in Fig. 1. From the perspective of saving more water and easier irrigation operation, it will be more effective to fallow the farms irrigated by the same canal even they are spatially apart. If the canal network system is overlaid on top of the fields, as shown in the upper part of Fig. 3, these two patterns show different aggregation characteristics from the irrigation management perspective. It can be observed that the pattern in Fig. 3b is much aggregated than that in Fig. 3a from the perspective of water distribution. The canal A can be shut off completely for fallow pattern in Fig. 3b and more water may be saved under this situation than that in Fig. 3a The original JCS definition cannot distinguish the differences between these two distribution patterns and needs to be modified to consider this underlying spatial relationship.
Modified JCS As shown in Eq. 2, a modified form of JCS is proposed to take into consideration the influences of the underlining irrigation system on spatial aggregation.
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Fig. 2 Examples of JCS application to farm fallow patterns. a–c Spatial patterns of three fallow scenarios; d–f show the calculated values of P P W X X for each cell and corresponding JCS indices for each scenarios ij i j i j
Fig. 3 Examplesof MJCS calculation for farm fallow patterns. a, b Fallow farms with the underlined irrigation network; c, d are calculated P P values of i j Wij Zij Xi Xj for each cell and the corresponding JCS indices; and e shows a scenario with all farms fallowed
P P i j ðWij Zij Xi Xj Þ MJCS ¼ P P i j ðWij Zij Þ
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ð2Þ
A new spatial connectivity factor Zij is introduced to differentiate the water supply sources delivered to the fields. As shown in Fig. 1, two fields are more likely to be
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irrigated by different water sources if they receive water from different main canals. The smallest weighting factor of Zij = 0 is assigned for this case. The definitions of Zij are summarized as follows: Zij = 0; if xi and xj are irrigated by different main canals (e.g., a–b in Fig. 1). Zij = 1; if xi and xj are irrigated by the same main canal but different sub-main canals (e.g., c–d, f–g in Fig. 1). Zij = 2; if xi and xj are irrigated by the same sub-main canal but different laterals (e.g., b–d, e–d, a–f in Fig. 1). Zij = 3; if xi and xj are irrigated by the same laterals but different tertiary ditches (e.g., a–h, b–e in Fig. 1).
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The cases shown in Fig. 3c–e are then modified so that the fields are irrigated by two separate main canals as shown in Fig. 4a–c. The MJCS are then calculated as 0.45 (=132/292), 0.56 (=164/292), and 1.0 (=292/292) for fallow patterns of Fig. 4a–c, respectively. The pattern in Fig. 4b with a higher MJCS value is much aggregated than MJCS of Fig. 4a. The WijZij can be thought as a compound weighting index for spatial connectivity to examine both the physical and underlined spatial adjacencies.
Case study
The main–submain–lateral-tertiary network hierarchy may be generalized as 1st, 2nd, 3rd, 4th level, and so on for some more complicated cases where there exits more than four levels of network hierarchy, and the Zij values can be greater than 3 as the level of network hierarchy becomes higher. Two fields Xi and Xj with higher Zij will more likely receive irrigation water from the same supply source. Namely, Zij acts as a surrogate to the hierarchical relationship of canal network system. The modified JCS is then standardized between 0 and 1 by the denominator of Eq. 2 for comparison purposes. The denominator of the equation represents the JCS for a special case with every field in fallow, and is used to make the MJCS values standardized indices between 0 and 1. The lower part of Fig. 3 shows the MJCS computations for some examples. Figure 3c, d are taken from the same ones shown in Fig. 3a, b. The numbers shown in each cells represent the values of Ri Rj Wij Zij Xi Xj for that cell. Figure 3e shows the extreme case that every cell is in fallow with MJCS = 376/376 = 1.0. The MJCS are calculated as 0.40 (=150/376) and 0.44 (=164/376) for the cases of Fig. 3c, d, respectively. The fallow pattern of Fig. 3d is more aggregated than that of Fig. 3c from the perspective of reducing irrigation demand.
The command area of the Chia-Nan Irrigation Association in Taiwan, as shown in Fig. 5, was used as a case study area to demonstrate the usefulness of the proposed modified JCS. With an area of more than 70 thousands hectares, this command area is the largest one in Taiwan. The water is delivered to the fields from the reservoir through a hierarchical network system. Three fallow scenarios with different degrees of spatial aggregation are shown in Fig. 6. The MJCS indices are calculated as 0.261, 0.180, and 0.151, respectively, for the fallow patterns shown in Fig. 6a–c. According to the definition and discussion above, the fallow scenario in Fig. 6a will be the most aggregated and also the most effective one in the sense of irrigation demand reduction. For comparison of the three scenarios, the MJCS were calculated and a previously published GIS-based regional irrigation demand estimation model (Wen et al. 2004) was used to estimate the irrigation demand reductions. The characteristics of crop, soil, climate, water conveyance, and irrigation methods are considered in this regional irrigation demand estimation model, and GIS is used to capture the spatial heterogeneity of these factors. The comparisons among the three fallow scenarios shown in Fig. 6 are summarized in Table 1. The fallow areas are 4484, 4408, and 4418 ha, respectively, for
Fig. 4 Examples of MJCS calculation for farms irrigated by different main canals. The numbers shown in the boxes calculated values of P P i j Wij Zij Xi Xj ; a shows a scenario with some farms fallowed in
canal A, B, and C; b shows a scenario with all farms fallowed in canal A and some farms fallowed in canal B; and c shows a scenario with all farms fallowed
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Fig. 5 Study area. a The command area of Chia-Nan irrigation association With Canal System. b The Shin-Hua Irrigation Management Division
Fig. 6 Case study 1: Fallow scenarios with different degrees of spatial aggregation. a The most aggregated one with all fallow areas in a single cluster. b One in mediate aggregated distribution, and c is the most dispersed pattern Table 1 Summary of scenario comparisons (case study 1)
* MJCS Ratio = MJCS Difference/MJCB of scenario 1
Scenario
MJCS
Fallow area (ha)
Irrigation demand reduction (106 m3)
Demand reduction per unit fallow area (106 m3/ha)
1
0.261
4,484
56.53
0.0126
2
0.181
4,408
54.81
0.0124
0.31
3
0.151
4,418
52.18
0.0118
0.42
scenario 1, 2, and 3. It is demonstrated that the higher MJCS representing more spatial aggregation and will save more water from irrigation demand reduction. The MJCS
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MJCS ratio*
shows that the first scenario is the most effective one, and this also confirmed by the calculated demand reduction per unit fallow area. The first scenario, with all the fallow
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area in one single cluster, saves the highest water from each fallow hectare. Although the fallow area in the second scenario is smaller, it cut more irrigation water demand than that of the third scenario. From the water
saving perspective, higher aggregation of fallow pattern is better because it will reduce more irrigation water demand and also is easier in the sense of irrigation management.
Fig. 7 Case study 2: Fallow scenarios with different degrees of hierarchical canals. a Fallow areas irrigated by a single lateral, b fallow areas irrigated by two different laterals, and c fallow areas P P irrigated by three different laterals; d–f show i j Wij Xi Xj values
for each polygons; g–i are polygons
P P i
j
Wij Zij Xi Xj
values for each
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38 Table 2 Summary of scenario comparisons (case study 2)
* MJCS Ratio = MJCS Difference/MJCB of scenario 1
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Fallow area (ha)
MJCS
1
8
0.049
684.39
946.25
1.38
2
8
0.041
1407.62
1753.23
1.25
0.17
3
8
0.039
1394.69
1739.32
1.25
0.21
Conclusions and discussions It is a difficult decision to make for where and how much to fallow if partial fallow is necessary to cut down the regional irrigation demand. Different spatial pattern of fallow scenarios may result in different irrigation demand reduction effectiveness due to the nonlinearity between the total fallow area and the irrigation demand reduction. A Fig. 8 The shape effect of spatial units on Joint Count Statistics. a Hexagon, b square, c triangle
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MJCS ratio*
JCS
The aggregation tendencies in scenarios shown in Fig. 6 are too obvious and the tradition JCS may also effectively distinguish among them. To demo the effectiveness of MJCS over the traditional JCS, an irrigation management division of the Chia-Nan Irrigation association as shown in Fig. 5b was used as another study case. Three fallow patterns are shown in Fig. 7a–c. The first one (Fig. 7a) is the most aggregated one with all fallow areas irrigated by a single lateral. Figure 7b shows a fallow area irrigated by two different laterals, and Fig. 7c is the most dispersed fallow pattern as perceived from the irrigation network that is irrigated by three different laterals. As shown in Fig. 7d–f, the tradition JCS were calculated as 8 for all of the three scenarios and cannot differentiate among the three fallow patterns. The MJCS were calculated to be 0.049, 0.041, and 0.039, respectively, in Fig. 7g–i as the canal network hierarchies were taken into account. The irrigation demand reduction per unit fallow area were also computed and summarized in Table 2. The case shown in Fig. 7g, with the highest MJCS, was evaluated as a better choice and was verified with the highest irrigation demand reduction per unit fallow area. The MJCS was proved to be more effective in capture of the spatial aggregation tendency when irrigation canal network hierarchy was considered.
Irrigation demand reduction (104 m3)
Demand reduction per unit fallow area (104 m3/ha)
Scenario
modified JCS was proposed to appraise proposed fallow scenarios in the drought mitigation process. From the studies of hypothetical examples as well as field case studies, the proposed MJCS are proved to be useful in detecting the clustering tendency when the spatial patterns are affected by another underlining spatial pattern. The spatial weighting indices Wij of traditional JCS were modified in this study to reflect the influence of an underlined irrigation canal network. This definition is good for tree type network systems like irrigation network or natural stream system. Further studies may be needed to define different transformation of Wij for other underlined spatial patterns such as traffic network, but the current version is effective to evaluate the decision effectiveness in partial fallow planning to adapt to drought situation. The traditional JCS depends on size and shape of polygons. If the farms are intentionally divided into smaller units, a larger JCS will results with the same fallow area. The proposed MJCS also have this same defect. Although most of the irrigation management units in Taiwan have roughly equal sizes, it must be emphasized that the application of MJCS should be based on this prerequisite of uniform unit sizes. The shapes of the spatial unit may also influence the JCS. As shown in Fig. 8, different shapes with the same spatial pattern may result in different JCS. The degree on influences may need more future study, but the MJCS may be used where the farm land consolidation has been done. Different region scale of study area may also influence the MJCS property. The sensitivity of the proposed MJCS may decrease as the scale of the study region becomes larger, but its capacity will still exist. The MJCS is designed to preserve the canal network hierarchy and its effectiveness will be higher as the network systems get
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more complicated (as the canal branching levels get up to 4 or higher). This scale effect can be observed from the MJCS ratios comparisons between Table 1 and Table 2. Regional irrigation demand is affected not only by the spatial pattern of farm distribution but also by the spatial variation of crop, soil, and climate. The proposed MJCS only considers the spatial distribution pattern and may not be used as a single index for choosing the most appropriate fallow farms. Field location is the single factor used in this study, but the activity/capacity (such as soil characteristics) also matter and Moran’s I or Geary’s C may be used for clustering tendency identification with these specific attribute characteristics. A future potential study is to include the network hierarchy into one of these two indices. Acknowledgments The authors wish to express their gratitude to Water Resource Agency and the Council of Agriculture of Taiwan for the financial support under project MOEAWRA0970054 and 98AS7.4.1-b1.
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