title: Boat electrofishing survey of the lower Waikanae River, Ratanui Lagoon, and Lake Waitawa

authors: Hicks, Brendan J.

subjects: New Zealand

abstract: We conducted the first electrofishing boat survey of the lower Waikanae River, Ratanui Lagoon, and Lake Waitawa on 11-12 July 2006. We caught five introduced and five native fish species in 4.74 km of fished length from a total of nine sites. Assuming that the bow-mounted anodes caught fish within a 1-m radius, the width fished was 4 m, and the total area fished was 16,200 m² or 1.62 ha.
We landed a total of 125 fish comprising five introduced and five native fish species at the nine fished sites (Table 3). Shortfin eels were the most numerous species but are mostly not included in this total. We did not bring eels on board because of the handling time this involved, except for two sites 263 and 264 where densities were 1.19 fish 100 m⁻², which is moderate density of eels compared to previous boat electrofishing one-pass estimates, perch, tench, and rudd were found at most sites in Lake Waitawa. Goldfish had a much more restricted distribution, and were caught at only one site. Four adult brown trout were caught in the lower Waikanae River. Because of their large size, adult brown trout and tench comprised a significant part of the fish biomass where they occurred.
No koi carp were caught, probably because of a combination of low density and low water temperature. Water temperature at the time of fish (10.2-10.5 °C in Lake Waitawa) may have influenced the susceptibility to koi carp to electrofishing. Common carp are known to seek winter refuge in deep water at temperatures below 11°C. Electrofishing is limited to the upper 3 m of the water column and would be ineffective if koi carp, Cyprinus carpio) are also less active during periods of low water. Inactivity reduces the probability of encountering fish and lowers catch rates. The optimal period for sampling koi carp begins as the water warms in spring, when koi carp move into the littoral shallows to spawn and are therefore highly visible. Common carp in Australia begin to spawn when water temperatures reach 15°C and koi carp have been observed spawning in New Zealand in Lake Waikare as early as 11 September in a water temperature 15.3°C. However, it is encouraging that no small koi carp were caught because this is evidence that breeding is not occurring in Lake Waitawa or Ratanui Lagoon, where koi carp are known to occur (Ian Cooksley, DOC, pers. comm.).
Previous fishing with the electrofishing boat in the North Island, in similar conductivities and habitats and with similar machine settings, has caught a full size range of eels, smelt, bullies, grey mullet, rudd, brown bullhead catfish, perch, tench, goldfish, and koi carp. Thus we believe that these results reflect an accurate picture of fish abundance in the Waikanae area but we acknowledge that fishing in spring or summer in higher water temperatures is likely to increase the likelihood of catching koi carp.
This fish data have been entered into NIWA’s New Zealand Freshwater Fish Database as card numbers 15190 to 15198.

text: Boat electrofishing survey of the lower Waikanae River, Ratanui Lagoon, and Lake Waitawa We conducted the first electrofishing boat survey of the lower Waikanae River, Ratanui Lagoon, and Lake Waitawa on 11-12 July 2006. We caught five introduced and five native fish species in 4.74 km of fished length from a total of nine sites. Assuming that the bow-mounted anodes caught fish within a 1-m radius, the width fished was 4 m, and the total area fished was 16,200 m² or 1.62 ha.
We landed a total of 125 fish comprising five introduced and five native fish species at the nine fished sites (Table 3). Shortfin eels were the most numerous species but are mostly not included in this total. We did not bring eels on board because of the handling time this involved, except for two sites 263 and 264 where densities were 1.19 fish 100 m⁻², which is moderate density of eels compared to previous boat electrofishing one-pass estimates, perch, tench, and rudd were found at most sites in Lake Waitawa. Goldfish had a much more restricted distribution, and were caught at only one site. Four adult brown trout were caught in the lower Waikanae River. Because of their large size, adult brown trout and tench comprised a significant part of the fish biomass where they occurred.
No koi carp were caught, probably because of a combination of low density and low water temperature. Water temperature at the time of fish (10.2-10.5 °C in Lake Waitawa) may have influenced the susceptibility to koi carp to electrofishing. Common carp are known to seek winter refuge in deep water at temperatures below 11°C. Electrofishing is limited to the upper 3 m of the water column and would be ineffective if koi carp, Cyprinus carpio) are also less active during periods of low water. Inactivity reduces the probability of encountering fish and lowers catch rates. The optimal period for sampling koi carp begins as the water warms in spring, when koi carp move into the littoral shallows to spawn and are therefore highly visible. Common carp in Australia begin to spawn when water temperatures reach 15°C and koi carp have been observed spawning in New Zealand in Lake Waikare as early as 11 September in a water temperature 15.3°C. However, it is encouraging that no small koi carp were caught because this is evidence that breeding is not occurring in Lake Waitawa or Ratanui Lagoon, where koi carp are known to occur (Ian Cooksley, DOC, pers. comm.).
Previous fishing with the electrofishing boat in the North Island, in similar conductivities and habitats and with similar machine settings, has caught a full size range of eels, smelt, bullies, grey mullet, rudd, brown bullhead catfish, perch, tench, goldfish, and koi carp. Thus we believe that these results reflect an accurate picture of fish abundance in the Waikanae area but we acknowledge that fishing in spring or summer in higher water temperatures is likely to increase the likelihood of catching koi carp.
This fish data have been entered into NIWA’s New Zealand Freshwater Fish Database as card numbers 15190 to 15198.

year: 2006

title: The structure and average discrepancies of lattice rules for numerical integration

authors: Reddy, Muni Vasudewan

abstract: Lattice rules are equal-weight quadrature rules which are used in the approximation of multidimensional integrands over the s-dimensional unit cube [0,1]ˢ.  One of the problems encountered in the study of such rules is the unavailability of a unique representation. It is known that any lattice rule may be expressed in a canonical D - Z form in which D is a diagonal matrix whose diagonal entries are known as the invariants and Z is an integer matrix. Although D is unique in this canonical form, Z may be chosen in many different ways. Except for the case of so-called projection-regular and prime-power rules, no such unique Z is available. In the latter case of prime-power rules, the unique D - Z form developed is known as an ultratriangular form. Associated with each ultratriangular form is a set of column indices. Any lattice rule may be decomposed into prime-power components. In this thesis, a unique D - Z form is defined for a special class of lattice rules for which the component prime-power rules have a consistent set of column indices. This new unique form includes the known unique forms for projection-regular and prime-power rules as special cases. We also use the ultratriangular form for prime-power lattice rules to derive a formula to calculate the number of prime-power rules having a given set of invariants and column indices. 

The existing theory of lattice rules that is based on the generator matrix of the dual lattice has made the assumption that its representation in the so-called Hermite normal form is upper triangular. However, since projection-regular rules have a unique Z-matrix which is unit upper triangular, the corresponding generator matrix for the dual lattice is lower triangular. This suggests that a lower triangular Hermite normal form might be appropriate for study. We consider this situation and give the conditions on the lower triangular Hermite normal form which allow a projection-regular rule to be easily recognized. 

Number-theoretic rules are a class of lattice rules which are known to be particularly suitable for the approximation of multidimensional integrals in which the integrands are periodic. In the case of non-periodic integrands there is numerical evidence that the average L₂ discrepancy for these rules is smaller than the expected value for Monte-Carlo rules when the dimension s is less than 18. For non-periodic integrands, a vertex-modified version of the number-theoretic rule has been previously proposed. In s-dimensions these vertex-modified rules contain 2ˢ weights which may be chosen optimally so that the discrepancy is minimized. We shall compare the average discrepancy for these optimal vertex-modified number-theoretic rules with that for normal number-theoretic and Monte-Carlo rules. A similar comparison is also carried out between the averages for number-theoretic rules and for 2ˢ copy rules with approximately the same number of points. 

In the case of periodic integrands it has been shown that the average of Pα and the values of R for 2ˢ copy rules are smaller than those for number-theoretic rules. For this periodic case, we use an analogue of the L₂ discrepancy to carry out a similar comparison.

text: The structure and average discrepancies of lattice rules for numerical integration Lattice rules are equal-weight quadrature rules which are used in the approximation of multidimensional integrands over the s-dimensional unit cube [0,1]ˢ.  One of the problems encountered in the study of such rules is the unavailability of a unique representation. It is known that any lattice rule may be expressed in a canonical D - Z form in which D is a diagonal matrix whose diagonal entries are known as the invariants and Z is an integer matrix. Although D is unique in this canonical form, Z may be chosen in many different ways. Except for the case of so-called projection-regular and prime-power rules, no such unique Z is available. In the latter case of prime-power rules, the unique D - Z form developed is known as an ultratriangular form. Associated with each ultratriangular form is a set of column indices. Any lattice rule may be decomposed into prime-power components. In this thesis, a unique D - Z form is defined for a special class of lattice rules for which the component prime-power rules have a consistent set of column indices. This new unique form includes the known unique forms for projection-regular and prime-power rules as special cases. We also use the ultratriangular form for prime-power lattice rules to derive a formula to calculate the number of prime-power rules having a given set of invariants and column indices. 

The existing theory of lattice rules that is based on the generator matrix of the dual lattice has made the assumption that its representation in the so-called Hermite normal form is upper triangular. However, since projection-regular rules have a unique Z-matrix which is unit upper triangular, the corresponding generator matrix for the dual lattice is lower triangular. This suggests that a lower triangular Hermite normal form might be appropriate for study. We consider this situation and give the conditions on the lower triangular Hermite normal form which allow a projection-regular rule to be easily recognized. 

Number-theoretic rules are a class of lattice rules which are known to be particularly suitable for the approximation of multidimensional integrals in which the integrands are periodic. In the case of non-periodic integrands there is numerical evidence that the average L₂ discrepancy for these rules is smaller than the expected value for Monte-Carlo rules when the dimension s is less than 18. For non-periodic integrands, a vertex-modified version of the number-theoretic rule has been previously proposed. In s-dimensions these vertex-modified rules contain 2ˢ weights which may be chosen optimally so that the discrepancy is minimized. We shall compare the average discrepancy for these optimal vertex-modified number-theoretic rules with that for normal number-theoretic and Monte-Carlo rules. A similar comparison is also carried out between the averages for number-theoretic rules and for 2ˢ copy rules with approximately the same number of points. 

In the case of periodic integrands it has been shown that the average of Pα and the values of R for 2ˢ copy rules are smaller than those for number-theoretic rules. For this periodic case, we use an analogue of the L₂ discrepancy to carry out a similar comparison.

year: 2000

title: Place-making: Wānanga based photographic approaches

authors: Hill, Rodrigo

subjects: photography

abstract: The words above are from the poem Māori King Tawhiao wrote expressing his love for his homelands of the Waikato and the region known today as the King Country. The words translate to: “I look down on the valley of Waikato, As though to hold it in the hollow of my hand.” Now imagine a large-scale photograph depicting a close-up frame of cupped hands trying to hold something carefully.

text: Place-making: Wānanga based photographic approaches The words above are from the poem Māori King Tawhiao wrote expressing his love for his homelands of the Waikato and the region known today as the King Country. The words translate to: “I look down on the valley of Waikato, As though to hold it in the hollow of my hand.” Now imagine a large-scale photograph depicting a close-up frame of cupped hands trying to hold something carefully.

year: 2022-12-31