Preliminary Look At The Exploitation Of The Spiny Lobster In The St Lucian Fishery
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A preliminary look at Exploitation of the Spiny Lobster Panulirus argus in the St. Lucian fishery. by Peter A. Murray and Sarah JenningsClark Department of Fisheries, Ministry of Agriculture, Lands, Fisheries, Forestry and Cooperatives, Castries, St. Lucia, W.I.. ABSTRACT This report presents preliminary analyses of data collected on landings of the Spiny Lobster, Panulirus argus, on the southeast coast of St. Lucia. The study was geared towards providing information pertinent to determining management strategies. Carapace lengths were measured, at one of the major lobster landing sites, during the lobster open season, arranged in 10 mm class intervals and inputted into the Compleat ELEFAN (Gayanilo, Soriano and Pauly, 1988) program package. Von Bertalanffy growth parameters were obtained using the method suggested by Murray and Nichols (1990). Estimates of current exploitation rate (E), exploitation rate at maximum sustainable yield per recruit (Emax), and exploitation rate at 10% of the slope (E0.1 ) were obtained. It would appear that the existing close season has served to keep the spiny lobster fishery on a stable footing notwithstanding the ever increasing demand.
Murray, P.A. and S. JenningsClark, 1994. A preliminary look at exploitation of the Spiny Lobster, Panulirus argus, in the St. Lucian Fishery. Proc. Gulf Caribb. Fish. Instit. 43: 685 689.
1
2
INTRODUCTION The Spiny Lobster, Panulirus argus, is an important resource in St. Lucia, being in great demand in the Tourist Industry. Management of the fishery is controlled by a close season having its basis in some unidentified studies of the past. The fishery has managed to survive despite rapid increases in demand since fishermen, in the main, adhere to the legal restrictions while being convinced that the basis of these restrictions may not be completely valid. The legally prescribed closed season runs from May 1st to August 31st in each year. There is a minimum legal carapace length of 95 mmCL coupled with a minimum legal total length of 250 mmTL. It is the general feeling of fishermen that, since spawning can be observed throughout the year and if in fact the closed season is based on the incidence of spawning, there should be no closed season or, at least, the closed period should be changed. While the Department of Fisheries has come to accept the possibility that the closed season may not be at the time of peak spawning activity, it is felt that some annual closure of the fishery is required. Goodwin et al. (1986) derived a value for Loo of 188 mmCL, K of 0.246 1 y and to of 0.26 y, for lobsters landed in St. Kitts. Aiken (1983) observed in Jamaica that from January to July most female lobsters were in spawning condition, with another increased spawning period in November. Cavalcante Soares and Lira Cavalcante (1985) observed similar major spawning periods in Brazil, with a peak in February. They also noted greater presence of egg bearing females between February and April coupled with a larger presence of juveniles from May to August with peaks in June July. These studies, conducted in other countries of the wider Western Central Atlantic region, provide useful bases for comparison with any results obtained in this study, which presents a preliminary analysis of data collected in a recent study of landings of lobster on the southeast coast of St. Lucia aimed at giving local information pertinent to determining management strategies. METHODS Carapace Length measurements were made on lobsters landed, on four days between the first day of the open seasons of 1989 and 1990 inclusive, at Savannes Bay to the southeast of St. Lucia. Measurements were taken from the forward edge of the carapace to the maximum concavity of it's rear edge. Data were arranged in 10mm class intervals and inputted into the Compleat ELEFAN program package (Gayanilo, Soriano and Pauly, 1988). The ELEFAN II routine was used to arrive at a first estimate of the von Bertalanffy growth parameter Loo (asymptotic length). This estimate was then used as the basis for another estimation of the parameters using the method suggested by Murray and Nichols (1990): in small steps, a wide range of values of the parameters K and Loo were scanned such as to identify the values associated with the highest value of the goodness of fit index, Rn, and any subpeaks. Combinations of the parameter estimates giving the highest values of Rn, were used to calculate probabilities of capture. Recruitment patterns were also derived with Pauly's empirical formula being used for estimating to ("age at length zero"; Pauly, 1979).
3 Sparre's version of the lengthconverted catch curve (pers. comm., cited in Pauly, 1984) was also used to obtain estimates of total mortality coefficient, Z, and exploitation rate, E. The latter were based on values of natural mortality coefficient, M, calculated by Pauly's (1980) empirical formula and assuming a mean annual environmental temperature of 27.5 o C. Yield per recruit analyses were also done using the probabilities of selection method (Pauly, 1984; Pauly and Soriano, 1986, cited in Gayanilo et al., 1988) built into the ELEFAN II routine. The Compleat ELEFAN package (Gayanilo et al., 1988) was used for all the preceeding determinations except for the calculation of to. RESULTS AND DISCUSSION Frequency distributions for the samples obtained are shown in Table 1. Growth parameter estimates for Loo and k are shown in Table 2; the combinations used and the values of to, Z, M and E derived, are shown in Table 3. The recruitment patterns obtained showed modes in September and December with the latter explaining over 80% of the recruitment. Emax estimates, as calculated, are also shown in table 3. The patterns of recruitment derived in this study appear to be consistent with both Aiken's (1983) and Cavalcante Soares and Lira Cavalcante's (1985) observations. Arellano (1989) notes values of the parameter Ø' (Pauly ad Munro, 1984) for the genus Panulirus having a mean value of 3.596 + 0.123 (a = 0.05) The Ó' values associated with the parameter combinations (see Table 4) are all outside this range, the combination of Loo = 191.0 and K = 0.850 being the farthest. The logic of ELEFAN I suggests that the value of K associated with the highest value of Rn is the prefered one, assuming that this value is part of a well defined, unique peak. The lack of small, fast growing lobsters in the samples (see Table 1) led to multiple peaks. From this it can be suggested that the actual magnitude of Rn may not be a reliable indicator of the value of K to be used. We feel that in this instance, the closeness of derived values of O' to the mean value for the genus (Arellano, 1989), is a more useful indicator. With this in mind, therefore, and considering the fact that the parameter combination having the Ø' value of 4.136 is reasonably close to those of Goodwin et al. (1986) the corresponding exploitation rate, when compared to the derived values of Emax and E0.1, suggest a reasonably healthy fishery. It must, however, be remembered that the exploitation rates estimated were calculated using values of natural mortality, M, derived from Pauly's (1980) empirical formula. The value of environmental temperature used in this formula was a mean yearly surface temperature. If one bears in mind the fact that lobsters are demersal, and assuming, even in the extreme for sake of argument, a 2.5 o C difference in temperature between the surface and (say) 30m below the surface, the overall picture differs very little. It appears therefore, is that the present exploitation rate is not posing a severe threat to the fishery. Within the context of the periodic closure of the fishery, it would appear that the existing close season has served to keep the fishery on a stable footing notwithstanding the everincreasing demand for lobster by St.
4 Lucia's expanding tourism sector. ACKNOWLEDGEMENTS We would like to thank Mr. Allan Smith of the Caribbean Natural Resources Institute (formerly ECNAMP) for his assistance both in terms of data collection and for his valuable comments on this paper. REFERENCES Aiken. K.A., 1983. Further investigation of the spiny lobster fishery of Jamaica. Pp. 177191 IN Western Central Atlantic Fishery Commission (WECAFC), 1983. National reports and selected papers presented at the third session of the Working Party on assessment of marine fishery resources. Kingston, Jamaica, 1721 May 1982. FAO Fish. Rep. 278 Suppl. Arellano, R.V., 1989. Estimation of growth parameters in Panulirus penicillatus using a Wetherall plot and comparisons with other lobsters. Fishbyte 7(2): 1315 Cavalcante Soares, C.N. and P.P. Lira Cavalcante, 1985. Caribbean spiny lobster (Panulirus argus) and Smoothtail spiny lobster (Panulirus laevicauda). Reproductive dynamics on the Brazilian Northeastern coast. Pp. 200217 IN Western Central Atlantic Fishery Commission (WECAFC), 1985. National reports and selected papers presented at the fourth session of the Working Party on assessment of marine fishery resources. Paipa, Department of Boyaca ', Colombia, 29 October 2 November 1983. FAO Fish. Rep. 327 Suppl. Gayanilo, F.C. Jr., M. Soriano and D. Pauly, 1988. A draft guide to the Compleat ELEFAN. ICLARM Software 2. International Center for Living Aquatic Resources Management, Manila, Philippines. 65pp. Goodwin, M.H., S.J. Heyliger and R.M. Wilkins, 1986. Progress report on the development of a management plan for the St. Kitts/Nevis Spiny lobster fishery. Manuscript report Fisheries Division, Ministry of Agriculture, Lands and Development. St. Kitts/Nevis. 19pp. Murray, P.A. and K.E. Nichols, 1990. Problems in estimating growth parameters of the Wahoo Acanthocybium solandri (Scombridae) using the ELEFAN I program. Fishbyte August 1990, pp.6 7 (in press).
5 Pauly, D., 1979. Gill size and temperature as governing factors in fish growth: a generalization of von Bertalanffy's growth formula. Ber. Inst. Meer. ChristianAlbrechts Univ., Kiel. 63: 156pp. Pauly, D., 1980. On the interrelationships between natural mortality, growth parameters and mean environmental temterature in 175 fish stocks. J. Cons. CIEM 39(3): 175192. Pauly, D., 1984. Lengthconverted catch curves: a powerful tool for fisheries research in the tropics (Part II). Fishbyte 2(1): 1719 Pauly, D. and J.L. Munro, 1984. Once more on growth comparisons in fish and aquatic invertebrates. Fishbyte 2(1):21
6 LIST OF TABLES Table 1. Frequency distribution of carapace lengths of Panulirus argus landed at Savannes Bay, Vieux Fort. Table 2.Growth parameter estimates for Panulirus argus based on landings sampled. Table 3. Growth parameter combinations used and parameters derived for Panulirus argus. Table 4.Growth parameter combinations and the coresponding values of Rn and Ø'.
7 Table 1.Frequency distribution of carapace lengths of Panulirus argus landed at Savannes Bay, Vieux Fort.
┌─────────────────┬────────────────────┬──────────────────────┐ │ Year │ 1989 │ 1990 │ ├─────────────────┼──────────┬─────────┼───────────┬──────────┤ │ Month/Day │ 09/01 │ 12/15 │ 01/04 │ 09/03 │ ├─────────────────┼──────────┼─────────┼───────────┼──────────┤ │ Midlength │ Number │ Number │ Number │ Number │ ├─────────────────┼──────────┼─────────┼───────────┼──────────┤ │ 75 │ 1 │ 0 │ 0 │ 1 │ │ │ │ │ │ │ │ 85 │ 31 │ 0 │ 0 │ 29 │ │ │ │ │ │ │ │ 95 │ 104 │ 5 │ 3 │ 57 │ │ │ │ │ │ │ │ 105 │ 79 │ 5 │ 0 │ 47 │ │ │ │ │ │ │ │ 115 │ 48 │ 6 │ 10 │ 29 │ │ │ │ │ │ │ │ 125 │ 17 │ 4 │ 9 │ 12 │ │ │ │ │ │ │ │ 135 │ 8 │ 3 │ 5 │ 3 │ │ │ │ │ │ │ │ 145 │ 4 │ 1 │ 1 │ 0 │ │ │ │ │ │ │ │ 155 │ 1 │ 0 │ 1 │ 1 │ │ │ │ │ │ │ │ 165 │ 0 │ 0 │ 1 │ 0 │ └─────────────────┴──────────┴─────────┴───────────┴──────────┘
8 Table 2Growth parameter estimates for Panulirus argus based on landings sampled.
╔══════════════════╦════════════════════╗ ║ Loo ║ K ║ ╟──────────────────╫────────────────────╢ ║ ║ ║ ║ 173.0 ║ 1.020 ║ ║ ║ ║ ║ 170.0 ║ 0.375 ║ ║ ║ ║ ║ 191.0 ║ 0.850 ║ ║ ║ ║ ║ ║ 0.540 ║ ║ ║ ║ ╚══════════════════╩════════════════════╝
9 Table 3.Growth parameter combinations used and parameters derived for Panulirus argus.
╔═════════════════╤══════════════════════════════════════════════════════╗ ║ Loo K │ too Z M E Emax E0.1 ║ ╟─────────────────┼──────────────────────────────────────────────────────╢ ║ │ ║ ║ 173.0 0.540 │ 0.186 2.219 1.380 0.378 0.676 0.651 ║ ║ │ ║ ║ 170.0 1.020 │ 0.097 4.476 2.102 0.530 0.662 0.604 ║ ║ │ ║ ║ 191.0 0.375 │ 0.264 2.141 1.057 0.506 0.656 0.615 ║ ║ │ ║ ║ 191.0 0.850 │ 0.113 4.853 1.806 0.628 0.639 0.605 ║ ║ │ ║ ╚═════════════════╧══════════════════════════════════════════════════════╝
10 Table 4.Growth parameter combinations and the corresponding values of Rn and Ø'. ╔═════════════════╤═════════════════╗ ║ Loo K │ Rn Ø' ║ ╟─────────────────┼─────────────────╢ ║ │ ║ ║ 173.0 0.540 │ 0.396 4.208 ║ ║ │ ║ ║ 170.0 1.020 │ 0.781 4.469 ║ ║ │ ║ ║ 191.0 0.375 │ 0.396 4.136 ║ ║ │ ║ ║ 191.0 0.850 │ 0.891 4.491 ║ ║ │ ║ ╚═════════════════╧═════════════════╝
Murray, P.A. and S. JenningsClark, 1994. A preliminary look at exploitation of the Spiny Lobster, Panulirus argus, in the St. Lucian Fishery. Proc. Gulf Caribb. Fish. Instit. 43: 685 689.
1
2
INTRODUCTION The Spiny Lobster, Panulirus argus, is an important resource in St. Lucia, being in great demand in the Tourist Industry. Management of the fishery is controlled by a close season having its basis in some unidentified studies of the past. The fishery has managed to survive despite rapid increases in demand since fishermen, in the main, adhere to the legal restrictions while being convinced that the basis of these restrictions may not be completely valid. The legally prescribed closed season runs from May 1st to August 31st in each year. There is a minimum legal carapace length of 95 mmCL coupled with a minimum legal total length of 250 mmTL. It is the general feeling of fishermen that, since spawning can be observed throughout the year and if in fact the closed season is based on the incidence of spawning, there should be no closed season or, at least, the closed period should be changed. While the Department of Fisheries has come to accept the possibility that the closed season may not be at the time of peak spawning activity, it is felt that some annual closure of the fishery is required. Goodwin et al. (1986) derived a value for Loo of 188 mmCL, K of 0.246 1 y and to of 0.26 y, for lobsters landed in St. Kitts. Aiken (1983) observed in Jamaica that from January to July most female lobsters were in spawning condition, with another increased spawning period in November. Cavalcante Soares and Lira Cavalcante (1985) observed similar major spawning periods in Brazil, with a peak in February. They also noted greater presence of egg bearing females between February and April coupled with a larger presence of juveniles from May to August with peaks in June July. These studies, conducted in other countries of the wider Western Central Atlantic region, provide useful bases for comparison with any results obtained in this study, which presents a preliminary analysis of data collected in a recent study of landings of lobster on the southeast coast of St. Lucia aimed at giving local information pertinent to determining management strategies. METHODS Carapace Length measurements were made on lobsters landed, on four days between the first day of the open seasons of 1989 and 1990 inclusive, at Savannes Bay to the southeast of St. Lucia. Measurements were taken from the forward edge of the carapace to the maximum concavity of it's rear edge. Data were arranged in 10mm class intervals and inputted into the Compleat ELEFAN program package (Gayanilo, Soriano and Pauly, 1988). The ELEFAN II routine was used to arrive at a first estimate of the von Bertalanffy growth parameter Loo (asymptotic length). This estimate was then used as the basis for another estimation of the parameters using the method suggested by Murray and Nichols (1990): in small steps, a wide range of values of the parameters K and Loo were scanned such as to identify the values associated with the highest value of the goodness of fit index, Rn, and any subpeaks. Combinations of the parameter estimates giving the highest values of Rn, were used to calculate probabilities of capture. Recruitment patterns were also derived with Pauly's empirical formula being used for estimating to ("age at length zero"; Pauly, 1979).
3 Sparre's version of the lengthconverted catch curve (pers. comm., cited in Pauly, 1984) was also used to obtain estimates of total mortality coefficient, Z, and exploitation rate, E. The latter were based on values of natural mortality coefficient, M, calculated by Pauly's (1980) empirical formula and assuming a mean annual environmental temperature of 27.5 o C. Yield per recruit analyses were also done using the probabilities of selection method (Pauly, 1984; Pauly and Soriano, 1986, cited in Gayanilo et al., 1988) built into the ELEFAN II routine. The Compleat ELEFAN package (Gayanilo et al., 1988) was used for all the preceeding determinations except for the calculation of to. RESULTS AND DISCUSSION Frequency distributions for the samples obtained are shown in Table 1. Growth parameter estimates for Loo and k are shown in Table 2; the combinations used and the values of to, Z, M and E derived, are shown in Table 3. The recruitment patterns obtained showed modes in September and December with the latter explaining over 80% of the recruitment. Emax estimates, as calculated, are also shown in table 3. The patterns of recruitment derived in this study appear to be consistent with both Aiken's (1983) and Cavalcante Soares and Lira Cavalcante's (1985) observations. Arellano (1989) notes values of the parameter Ø' (Pauly ad Munro, 1984) for the genus Panulirus having a mean value of 3.596 + 0.123 (a = 0.05) The Ó' values associated with the parameter combinations (see Table 4) are all outside this range, the combination of Loo = 191.0 and K = 0.850 being the farthest. The logic of ELEFAN I suggests that the value of K associated with the highest value of Rn is the prefered one, assuming that this value is part of a well defined, unique peak. The lack of small, fast growing lobsters in the samples (see Table 1) led to multiple peaks. From this it can be suggested that the actual magnitude of Rn may not be a reliable indicator of the value of K to be used. We feel that in this instance, the closeness of derived values of O' to the mean value for the genus (Arellano, 1989), is a more useful indicator. With this in mind, therefore, and considering the fact that the parameter combination having the Ø' value of 4.136 is reasonably close to those of Goodwin et al. (1986) the corresponding exploitation rate, when compared to the derived values of Emax and E0.1, suggest a reasonably healthy fishery. It must, however, be remembered that the exploitation rates estimated were calculated using values of natural mortality, M, derived from Pauly's (1980) empirical formula. The value of environmental temperature used in this formula was a mean yearly surface temperature. If one bears in mind the fact that lobsters are demersal, and assuming, even in the extreme for sake of argument, a 2.5 o C difference in temperature between the surface and (say) 30m below the surface, the overall picture differs very little. It appears therefore, is that the present exploitation rate is not posing a severe threat to the fishery. Within the context of the periodic closure of the fishery, it would appear that the existing close season has served to keep the fishery on a stable footing notwithstanding the everincreasing demand for lobster by St.
4 Lucia's expanding tourism sector. ACKNOWLEDGEMENTS We would like to thank Mr. Allan Smith of the Caribbean Natural Resources Institute (formerly ECNAMP) for his assistance both in terms of data collection and for his valuable comments on this paper. REFERENCES Aiken. K.A., 1983. Further investigation of the spiny lobster fishery of Jamaica. Pp. 177191 IN Western Central Atlantic Fishery Commission (WECAFC), 1983. National reports and selected papers presented at the third session of the Working Party on assessment of marine fishery resources. Kingston, Jamaica, 1721 May 1982. FAO Fish. Rep. 278 Suppl. Arellano, R.V., 1989. Estimation of growth parameters in Panulirus penicillatus using a Wetherall plot and comparisons with other lobsters. Fishbyte 7(2): 1315 Cavalcante Soares, C.N. and P.P. Lira Cavalcante, 1985. Caribbean spiny lobster (Panulirus argus) and Smoothtail spiny lobster (Panulirus laevicauda). Reproductive dynamics on the Brazilian Northeastern coast. Pp. 200217 IN Western Central Atlantic Fishery Commission (WECAFC), 1985. National reports and selected papers presented at the fourth session of the Working Party on assessment of marine fishery resources. Paipa, Department of Boyaca ', Colombia, 29 October 2 November 1983. FAO Fish. Rep. 327 Suppl. Gayanilo, F.C. Jr., M. Soriano and D. Pauly, 1988. A draft guide to the Compleat ELEFAN. ICLARM Software 2. International Center for Living Aquatic Resources Management, Manila, Philippines. 65pp. Goodwin, M.H., S.J. Heyliger and R.M. Wilkins, 1986. Progress report on the development of a management plan for the St. Kitts/Nevis Spiny lobster fishery. Manuscript report Fisheries Division, Ministry of Agriculture, Lands and Development. St. Kitts/Nevis. 19pp. Murray, P.A. and K.E. Nichols, 1990. Problems in estimating growth parameters of the Wahoo Acanthocybium solandri (Scombridae) using the ELEFAN I program. Fishbyte August 1990, pp.6 7 (in press).
5 Pauly, D., 1979. Gill size and temperature as governing factors in fish growth: a generalization of von Bertalanffy's growth formula. Ber. Inst. Meer. ChristianAlbrechts Univ., Kiel. 63: 156pp. Pauly, D., 1980. On the interrelationships between natural mortality, growth parameters and mean environmental temterature in 175 fish stocks. J. Cons. CIEM 39(3): 175192. Pauly, D., 1984. Lengthconverted catch curves: a powerful tool for fisheries research in the tropics (Part II). Fishbyte 2(1): 1719 Pauly, D. and J.L. Munro, 1984. Once more on growth comparisons in fish and aquatic invertebrates. Fishbyte 2(1):21
6 LIST OF TABLES Table 1. Frequency distribution of carapace lengths of Panulirus argus landed at Savannes Bay, Vieux Fort. Table 2.Growth parameter estimates for Panulirus argus based on landings sampled. Table 3. Growth parameter combinations used and parameters derived for Panulirus argus. Table 4.Growth parameter combinations and the coresponding values of Rn and Ø'.
7 Table 1.Frequency distribution of carapace lengths of Panulirus argus landed at Savannes Bay, Vieux Fort.
┌─────────────────┬────────────────────┬──────────────────────┐ │ Year │ 1989 │ 1990 │ ├─────────────────┼──────────┬─────────┼───────────┬──────────┤ │ Month/Day │ 09/01 │ 12/15 │ 01/04 │ 09/03 │ ├─────────────────┼──────────┼─────────┼───────────┼──────────┤ │ Midlength │ Number │ Number │ Number │ Number │ ├─────────────────┼──────────┼─────────┼───────────┼──────────┤ │ 75 │ 1 │ 0 │ 0 │ 1 │ │ │ │ │ │ │ │ 85 │ 31 │ 0 │ 0 │ 29 │ │ │ │ │ │ │ │ 95 │ 104 │ 5 │ 3 │ 57 │ │ │ │ │ │ │ │ 105 │ 79 │ 5 │ 0 │ 47 │ │ │ │ │ │ │ │ 115 │ 48 │ 6 │ 10 │ 29 │ │ │ │ │ │ │ │ 125 │ 17 │ 4 │ 9 │ 12 │ │ │ │ │ │ │ │ 135 │ 8 │ 3 │ 5 │ 3 │ │ │ │ │ │ │ │ 145 │ 4 │ 1 │ 1 │ 0 │ │ │ │ │ │ │ │ 155 │ 1 │ 0 │ 1 │ 1 │ │ │ │ │ │ │ │ 165 │ 0 │ 0 │ 1 │ 0 │ └─────────────────┴──────────┴─────────┴───────────┴──────────┘
8 Table 2Growth parameter estimates for Panulirus argus based on landings sampled.
╔══════════════════╦════════════════════╗ ║ Loo ║ K ║ ╟──────────────────╫────────────────────╢ ║ ║ ║ ║ 173.0 ║ 1.020 ║ ║ ║ ║ ║ 170.0 ║ 0.375 ║ ║ ║ ║ ║ 191.0 ║ 0.850 ║ ║ ║ ║ ║ ║ 0.540 ║ ║ ║ ║ ╚══════════════════╩════════════════════╝
9 Table 3.Growth parameter combinations used and parameters derived for Panulirus argus.
╔═════════════════╤══════════════════════════════════════════════════════╗ ║ Loo K │ too Z M E Emax E0.1 ║ ╟─────────────────┼──────────────────────────────────────────────────────╢ ║ │ ║ ║ 173.0 0.540 │ 0.186 2.219 1.380 0.378 0.676 0.651 ║ ║ │ ║ ║ 170.0 1.020 │ 0.097 4.476 2.102 0.530 0.662 0.604 ║ ║ │ ║ ║ 191.0 0.375 │ 0.264 2.141 1.057 0.506 0.656 0.615 ║ ║ │ ║ ║ 191.0 0.850 │ 0.113 4.853 1.806 0.628 0.639 0.605 ║ ║ │ ║ ╚═════════════════╧══════════════════════════════════════════════════════╝
10 Table 4.Growth parameter combinations and the corresponding values of Rn and Ø'. ╔═════════════════╤═════════════════╗ ║ Loo K │ Rn Ø' ║ ╟─────────────────┼─────────────────╢ ║ │ ║ ║ 173.0 0.540 │ 0.396 4.208 ║ ║ │ ║ ║ 170.0 1.020 │ 0.781 4.469 ║ ║ │ ║ ║ 191.0 0.375 │ 0.396 4.136 ║ ║ │ ║ ║ 191.0 0.850 │ 0.891 4.491 ║ ║ │ ║ ╚═════════════════╧═════════════════╝
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