reid page magnitude frequency new zeland

8/6/2019 Reid Page Magnitude Frequency New Zeland

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Magnitude and frequency of landsliding in a large New Zealand catchment

L.M. Reid a,*, M.J. Page b,1

a USDA Forest Service, Pacific Southwest Research Station, Arcata, CA, USA b Landcare Research, Private Bag 11-052, Palmerston North, New Zealand

Received 13 July 1998; received in revised form 2 April 2002; accepted 17 April 2002

Abstract

Knowledge of long-term average rates of erosion is necessary if factors affecting sediment yields from catchments are to beunderstood. Without such information, it is not possible to assess the potential influence of extreme storms, and, therefore, toevaluate the relative importance of various components of a sediment budget. A study of the sediment budget for the Waipaoacatchment, North Island, New Zealand, included evaluation of long-term rates of landsliding for six landslide-prone landsystems in the catchment. The number of landslides per unit area generated by each of several storms was counted on sequentialaerial photographs and correlated with the magnitude of the corresponding storm. The resulting relationships were combinedwith magnitudefrequency relationships derived for storms from 70- to 100-year rainfall records in the area to estimate a long-

term magnitude frequency relationship for landsliding for each land system. The long-term average values of the areallandslide frequency (number of slides per unit area per unit time) were then calculated from these relationships. The volumes of a sample of landslide scars were measured in the field, and the proportion of slides that deliver sediment to channels wasdetermined from aerial photographs. These measurements then allowed calculation of the long-term average rate of sediment production to streams from landslides for different land systems and types of vegetation. Results suggest that shallow landslidescurrently contribute about 15 F 5% of the suspended sediment load in the Waipaoa River above the Kanakanaia gauging station,and that 75% of the sediment production from the landslides occurs during storms with recurrence intervals of less than 27years. Reforestation of 6.3% (93 km 2) of the slide-prone lands in the catchment between 1990 and 1995 resulted in a calculateddecrease in slide-derived sediment of 10%. Calculations suggest that reforestation of an additional 3% (66 km 2) of thecatchment in areas with the most sensitive combinations of land system and storm regime could decrease the total sediment inputs from landsliding by about 20%.D 2002 Elsevier Science B.V. All rights reserved.

Keywords: Landslides; Sediment budget; Sediment yield; Land-use impact; Magnitude frequency

1. Introduction

Shallow landsliding is an important erosion proc-ess in the soft-rock hill country of New Zealand(Crozier, 1986) . The frequency and severity of land-sliding are of particular concern in the Waipaoa catch-ment, North Island, New Zealand (Fig. 1) , because

0169-555X/02/$ - see front matter D 2002 Elsevier Science B.V. All rights reserved.PI I : S0169-555X(02)00164-2

* Corresponding author. Fax: +1-707-825-2901. E-mail addresses: [email protected] (L.M. Reid),

[email protected] (M.J. Page).1 Fax: +64-6-355-9230.

www.elsevier.com/locate/geomorphGeomorphology 49 (2002) 7188


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landslides strongly influence land-use activities there.Landsliding decreases pasture productivity by remov-ing fertile topsoil and reducing the reservoir for soil-

moisture storage, and increases the cost of farming bydamaging fences, roads, and reservoirs. Sediment contributed by landslides degrades the water quality

Fig. 1. Distribution of land systems prone to landsliding in the Waipaoa catchment.

L.M. Reid, M.J. Page / Geomorphology 49 (2002) 718872


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and aquatic ecosystems of the Waipaoa River, con-tributes to channel aggradation and related flooding of high-value agricultural lands, and accelerates siltation

of the harbor and of coastal habitats important tocommercial fisheries.Concern about impacts from landslide-related sedi-

ment has contributed to interest in reforesting portionsof the Waipaoa catchment. More information wasneeded, however, before the effectiveness of refores-tation for reducing sediment-related problems could be predicted. In particular, we needed to know the proportional contribution of landsliding to the totalsediment load in the Waipaoa River, the relativeimportance of different portions of the landscape ingenerating landslides, and the extent to which refor-estation reduces landsliding. A study of the sediment budget for the Waipaoa catchment was designed to provide this information. It quickly became evident that the relative importance of the largest stormswould have to be evaluated if recent observations of the rates of erosion were to be used to estimate rates of sediment input over a period long enough to account for inter-annual variations. Cyclone Bola h ad trig-gered very high rates of landsliding in 1988 (Page et al., 1999) , so we were concerned that the rate meas-ured from a 45-year span of sequential aerial photo-

graphs would overestimate that characteristic of thearea since European settlement.

Shallow landslides are usually triggered by high-intensity rainfall, and major tropical cyclones typi-cally cause extensive landsliding in the soft-rock hillcountry of New Zealand. The obvious association between high-intensity storms and landslides has ledresearchers in the region to construct a variety of relationships for use in landslide assessments.Researchers have identified intensities of storms that trigger landslides (Eyles, 1979; Crozier, 1996; Glade,

1996) and flood magnitudes associated with landslide-generating storms (Kelliher et al., 1995) ; relationshipshave been identified between the frequency of land-slide-generating storms and mean annual rainfall(Hicks, 1995) ; and storm rainfalls have been corre-lated with landslide frequencies (Omura and Hicks,1991) and thicknesses of deposits (Page et al., 1994a) .The success of such studies suggested that a similar approach could be used to calculate the long-termaverage contribution from shallow landslides to thesediment load of the Waipaoa River.

This paper describes construction of relationships between storm magnitudes and rates of landsliding for different landscape units in the Waipaoa catchment.

Results are used to calculate the average rate of sediment production from landsliding and to predict the likely effects of reforestation on sediment produc-tion from landslides. We then evaluate the sensitivityof results to various potential sources of error.

2. Study area

Informat ion from the Ne w Zealand Land ResourceInventory (Fletcher, 1988) was used to divide the2205-km 2 Waipaoa catchment into 16 landscape unitshere referred to as land systems, each with a uniquecombination of rock type, landforms, erosion pro-cesses, drainage density, and channel morphology.Six of these land systems are characterized by shallowlandsliding as an important erosion process. These sixsystems have a combined area of 1483 km 2, or 67% of the total catchment area.

Of the six land systems, the Te Arai exhibits thehighest density of landslides and is the most wide-spread, comprising 23% of the catchment. The TeArai land system occurs on weakly c onsolidate d mud-

stone of Miocene to Pliocene age (Table 1) . Theserocks exhibit closely spaced fractures and weather readily on exposure; surface frittering is common onfreshly exposed outcrops. A thin, discontinuous layer of tephra is present on uneroded sites. Soils generallyhave a silt fraction of 50% to 70%, and soil depth ishighly variable, ranging from a meter or two on ridgesto zero on recently eroded slopes. Most Te Araihillslopes are convexo-concave, with narrow, roundedridge crests; straight, landslide-scarred midslopes; andconcave, colluvial footslopes (Fig. 2) . Hillslopes typ-

ically have gradients of 20j

to 40j

and lengths of 50to 200 m. Hillslope surfaces are broken by landslidescars, shallow earthflows, and occasional linear gul-lies. Drainage density is about 3.8 km km

2, and most channels of third order or larger are incised intoterrace deposits of alluvial silts and gravels.

The Waingaromia land system differs from the TeArai in that mudstones are more crushed and sheared,hillslopes have lower gradients, and gullying is locallysevere. In the Makomako land system, bedrock con-sists of alternating thick layers of mudstone and thin

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layers of sandstone, hillslope gradients are steeper than in the Te Arai system, and the relatively planar

slopes feed directly into channels. Hillslope profilesin the Waihora land system are similar to those in theMakomako system, but the Waihora system is under-lain by massive to poorly bedded siltstone. Whareratahillslopes are formed from massive to bedded sand-stones, and gradients typically are steeper than thoseof Te Arai hillslopes. Hillslopes in the Wharekopaeland system are of a distinctively rolling character and are of lower gradient. Wharekopae bedrock ranges from massive and bedded sandstones to mud-stones and is covered by a relatively thick layer of

tephra. The Wharekopae land system shows the least evidence of erosion of the six systems consideredhere. Measurements of the bulk density of soils inthe area (Malcolm McLeod, unpublished data) indi-cate an average density of about 1250 kg m

3 for allsoils but those of the tephra-mantled Wharekopaelands, where a value of 1040 kg m

3 has beenmeasured.

An additional 20% of the Waipaoa catchment isaccounted for by seven other land systems that also produce occasional shallow landslides. Landslide fre-

quencies in these systems are lower or equal to thoseobserved in the Wharekopae land system. Shallow

landsliding is insignificant in the remaining three landsystems.

Most shallow landslides in the area are planar failures that remove only soil and a thin layer of weathered bedrock. About 55% of the failures are 0.5to 0.9 m in depth and less than 200 m 2 in area. Thedisplaced sediment evacuates the scar as a highlymobile flow that leaves a thin debris tail of mudon the hillslope surface. Some flows terminate wherea decrease in hillslope gradient allows deposition or at the point that the debris tail has depleted the available

sediment; the rest deliver a portion of the sediment toa channel.Average annual rainfall in the Waipaoa catchment

ranges from about 1000 mm on the coast near Gisborne to 2500 mm at the headwaters. Rainfall isunevenly distributed through the year, with 40% to45% of the annual precipitation falling during thewinter months of May through August. Most winter storms are of low intensity and long duration. Incontrast, tropical cyclones occasionally bring rainsof very high intensity and relatively short duration

Table 1Characteristics of hillslopes, vegetation, landslides, and analyses for each land system

Te Arai Waingaromia Makomako Waihora Wharerata Wharekopae

Area (km2

) 513 29 138 78 278 448 Bedrock type mudstone mudstone mudstone siltstone sandstone sandstone,mudstone

Vegetation cover percentage (as of 1995)Pasture a 86 14 69 59 67 80Exotic forest 12 86 22 28 14 14 Native forest, scrub 2 0.5 9 14 19 6Slide volume (m 3 ) 210 210 b 210 b 140 450 130Sliderain relation: slides/km 2 =a (storm magnitude)+b Number of samples 11 (3)c (4)c (6)d (10)d 11Slide threshold (mm) 150 200 200 150 150 125Value of a 0.72 0.37 0.37 0.22 0.22 0.098Value of b 108 73 73 33 33 12

Landslide frequency on pasture e (slides km

2 year

1 ) 28 20 10 18 10 8Sediment delivery by pasture landslides e (t km

2 year 1 ) 3700 2600 1300 1600 2800 530

a Small areas mapped as bare are included in the pasture category. b Dimensions of Waingaromia and Makomako slides are assumed to equal those of Te Arai slides.c Relationships for Waingaromia and Makomako are not significantly different, so data sets are combined.d Relationships for Wharerata and Waihora are not significantly different, so data sets are combined.e Calculated per unit area of the land system, given the distribution of storm regimes. Higher areas tend to be reforested first, so average

rates for pasture will tend to decrease as reforestation progresses.



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during March through May. Both kinds of stormshave triggered landsliding in the area, as have more

localized, brief, high-intensity convective storms.Most of the Waipaoa catchment was still covered

by primary indigenous forest when European settle-ment began in the 1830s, although areas of scrub,fern, and secondary forest were present on foothillsaround the Gisborne Plains where the Maori popula-tion was centered. Pollen records from Lake Repon-gaere, located 20 km west of Gisborne, indicate that the original podocarpbroadleaf forest in these low-land areas was burned and replaced by bracken andscrub soon after Maori settlement, about 650 years

ago (J. Wilmshurst, Landcare Research, Lincoln, NewZealand, personal communication). Europeans had begun to log and burn the hill country to establish pastures by 1870, and clearing was nearly complete by 1920. In the 1960s, areas of pasture began to be planted in exotic forest (principally Pinus radiata ) for soil conservation and timber production. By 1995,about 76% of the six slide-prone land systems sup- ported pastoral farming, exotic forest covered 16%,and most of the remaining 8% was scrub or indige-nous forest.

3. Methods

This study was designed to evaluate the contribu-tion of shallow landsliding to the sediment load of theWaipaoa River and to assess the extent to whichconversion of pasture to forest might reduce that contribution. It was necessary to (1) determine theaverage rate of landsliding for the catchment; (2)evaluate the sediment delivery ratio for shallow land-slides; and (3) evaluate the influence of reforestationon the average rate of sediment production fromlandslides. Because the size and timing of futurestorms is not knowable, the measure used for compar-

ing past and future effects must be independent of short-term weather patterns. This requirement is par-ticularly important because a cyclone with a recur-rence interval of about 100 years occurred in 1988.Long-term average rates were selected as the basis for comparison so that the relative influence of high-magnitude storms could be evaluated.

Twenty representative subcatchments in or adja-cent to the Waipaoa catchment were chosen for analysis on the basis of proximity to rain gauges,existence of aerial photographs, and location along a

Fig. 2. Landslides generated by Cyclone Bola on typical hillslopes in the Te Arai land system.



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gradient of rainfall intensities for Cyclone Bola. The100- to 1500-ha subcatchments have a combined areaequivalent to 10% of the pasture area in the six land

systems within the Waipaoa catchment. Nine forestedsites in five of the land systems were also evaluated;these represent 11% of the area in native forest andscrub in the six land systems in 1995. Because most of these remnant forest blocks are small (15 to 100 ha),rates of landsliding within the blocks are undoubtedlyinfluenced by the condition of surrounding lands.Only in the two largest blocks (154 and 800 ha) areoutside influences likely to be minimal.

Fresh landslide scars were counted in each samplearea on 1:17500- to 1:46600-scale aerial photographsusing a stereoscope with 6-fold magnification. Fifteensets of aerial photographs covered all or part of thecatchment, with a maximum of 7 sets at any one site.Most sites are represented by one to three sets of photographs. Counts were made for Cyclone Bolarainfalls of between 350 and 800 mm and for earlier storms with rainfalls between 100 and 356 mm.Unvegetated and partially vegetated debris depositsremained visible on photographs taken before thethird winter after landsliding, so the appearance of deposits allowed landslides from storms that hadoccurred within about 2 years of the imagery to be

distinguished from those triggered by earlier storms.Of the landslides inventoried, 94% had occurredduring the same calendar year as the photography.In two cases, slides from 4 years earlier were identi-fied on the basis of the freshness of the scars and lack of other storms large enough to trigger the slides.

Landslide scars from Cyclone Bola were clearlydefinable in the field 8 years after the storm, whenfieldwork was carried out. The volumes of 95 land-slide scars were calculated from field measurementsof scar depths and areas. In addition, landslides with

surface areas larger than 920 m2

and those larger than1150 m 2 (corresponding to volumes greater than 700and 870 m 3, respectively) were counted in represen-tative subcatchments to allow better definition of thecumulative frequency distributions for the largest slides.

The logarithms of the landslide volumes approx-imately fit normal probability distributions, indicatingthat extrapolation of the cumulative frequency distribution for volumes in each land system is likely to provide reasonable estimates of the frequencies of the

largest slides. Average volumes were calculated for landslides in each land system by multiplying the proportion of slides in each volume interval by the

average volume in that interval and summing theresults. Calculated mean volumes range between130 m3 for Wharekopae landslides and 450 m 3 for Wharerata landslides. Field measurements were not made for either Waingaromia or Makomako land-slides, but observations suggest that these slides aresimilar to those on Te Arai lands, where rock typesand hillslope morphologies are similar. On this basis,Waingaromia and Makomako landslides were as-signed the mean value of 210 m 3 calculated for TeArai landslides.

Records of daily rainfall were analyzed for two purposes. First, landslide densities for each photo-graphic interval were to be correlated with the mag-nitude of the storm that generated the landslides.Storm rainfall can vary widely through a large catch-ment even during the most spatially extensive storms,so records from the gauges nearest each sampledsubcatchment were examined to characterize each of the landslide-generating storms for each site. Stormmagnitude was defined for this study as the sum of daily rainfalls during a period bounded by days withless than 10 mm of rain. Given the variety of indices

that have been successfully related to landsliding inthe past (e.g., Eyles, 1979; Hicks, 1995; Kelliher et al., 1995; Crozier, 1996; Glade, 1996 ), many other indices could have been used as readily.

The second analysis of rainfall evaluated the long-term frequency distribution of the selected index of storm magnitude. Because average annual precipita-tion varies by a factor of 2 through the Waipaoacatchment and because the topography of the catch-ment influences the distribution of particular kinds of storms, frequency distributions had to be described for

different parts of the catchment. The frequency char-acteristics of the largest storms were of particular interest, so analysis depended primarily on the length-iest records of rainfall.

Rainfall records spanning 70 or more years wereavailable for four locations in the catchment (Fig. 3) .The magnitude of each storm was calculated from therainfall records for each site, and the frequencyassociated with each magnitude was calculated bydividing the number of storms of equal or higher magnitude by one more than the number of years of



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record at the site (Dunne and Leopold, 1978) . Becausedata from partial duration series were used, a theoret-ical distribution was not assumed. The same analysis

was carried out for nine other records of shorter duration (17 to 54 years) from gauges well-distributedthrough the catchment. The portions of the longer-duration records that correspond to the years of recordfor the short-record gauges were reanalyzed andcompared with each short-duration record to deter-mine whether storm characteristics at the short-recordsites are similar to those at the long-record sites. For example, if the magnitudefrequency relation for ashort-record site is based on records from 1949 to1990, relations for the four long-record sites wererecalculated using data only from 1949 to 1990. If theshort-record relation is approximately collinear withone of the abbreviated long-record relations, thecorresponding unabbreviated long-record relation isassumed to apply to the short-record site. If none of the long-record sites is collinear, the correspondinglong-record relation is estimated for the site by assum-ing that the long-term relations have the same propor-tional relationship as the short-term relations if theforms of the short-term relations are similar at twosites.

This analysis resulted in the definition of eight

magnitudefrequency curves applicabl e to dif ferent portions of the Waipaoa catchment (Fig. 3) . Therelations fall into two broad categories, one generally

characteristic of lowland stations and the other of

upland stations. Within each category, variationsreflect the gradient in annual precipitation. Amongthe lowland regimes, for example, the Waipaoa Sta-tion regime receives 1.8 times as much precipitation instorms of greater than 100 mm as the Gisborneregime. Because comparison of relations betweenstations suggests that orographic influences on stormcharacteristics are strong, and because the relationsreflect differences in total annual precipitation, whichalso varies by elevation, boundaries between stormregimes were drawn to approximate topographic con-

tours (Fig. 4) .

4. Average frequencies of landslides

The analysis strategy was based on that described by Reid (1998) : relationships are defined betweenstorm magnitudes and the associated areal landslidedensities, and these relationships can then be used toestimate average rates of landsliding from informationabout the magnitude frequency distribution of storms.

Fig. 4. Distribution of storm regimes in the Waipaoa catchment.Dots indicate locations of rain gauges used in the analysis; circleddots indicate gauges with records spanning more than 70 years.

Fig. 3. Expected frequency of storms as a function of stormmagnitude for storm regimes present in the Waipaoa catchment.



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In the present study, only the young scars on each photo set were catalogued to develop the relationships,allowing scars to be associated with particular storms

rather than with the distribution of storms occurringwithin a photographic interval. This approach avoidsthe need to identify the lengths of time over whichscars of different sizes remain visible on the air photos.In one case, two storms of similar intensity hadoccurred during the previous year, and the fresh land-slide scars were apportioned equally between the twostorms. In two other cases, fresh scars of two gener-ations could be discerned on the basis of the visibility

of debris tails or the extent of revegetation, so theeffects of two storms could be distinguished on thesame imagery.

Photographs from some years showed no scarswith debris tails visible, so the largest storm in the 2years preceding the photography had been below thethreshold for generating slides. Comparison of themagnitudes of the largest storms that did not generatelandslides with those of the smallest landslide-gener-ating storms suggests that only storms with magni-tudes of greater than about 150 mm are likely togenerate shallow landslides on Te Arai, Waihora, and

Fig. 5. Relationship between storm magnitude and areal landslide density for forest and pasture on landslide-prone land systems. Curved linesindicate the 95% confidence interval for the unconstrained regressions (solid lines), and bold dashed lines indicate regressions constrained to fit observations of threshold magnitudes for landslide generation. Maximum magnitudes for which landslides were not generated are indicated byarrows on the x-axis.



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Wharerata lands (maximum storms without land-slides: 108, 146, 179, 180 mm; minimum storms withlandslides: 131, 161, 161 mm). Threshold values for

Wharekopae landslides appear to be lower (maximumstorm without slides: 125 mm; minimum with slides:129 mm), and those for Waingaromia and Makomakolandslides higher (maximum storms without slides:147, 147 mm; minimum with slides: 229 mm).

For each land system, the areal landslide densities(numbers of slides per unit area) in pasture, asmeasured on aerial photographs, were regressedagainst the magnitudes of the storms assumed to have produced them. The regression equations for Te Araiand Wharekopae landslides are significantly different from those of al l other land systems at the 95%confidence level (Fig. 5). Equations for Wharerataand Waihora landslides are not significantly different from one another, so data were combined to construct a single relationship applicable to both land systems.Data sets from Makomako and Waingaromia landsystems were also indistinguishable from one another,and these data sets, too, were combined. The regres-sion equations explain 65% to 90% of the variance of observed areal landslide densities, but the equationstend to misrepresent the minimum magnitudes for storms that were observed to trigger landsliding. For

Wharekopae, for example, the regressed thresholdwas calculated to be 70 mm, while the observedthreshold lies between 125 and 129 mm. Equationswere recalculated assuming a threshold value of 150mm for Te Arai, Waihora, and Wharerata lands; 125mm for Wharekopae; and 200 mm for Waingaromiaand Makomako ( Table 1 , Fig. 5). The constrainedregressions each fall well within the 95% confidence bounds for the unconstrained regressions.

Long-term averages for the areal landslide fre-quency (number of slides per unit area per unit time)

generated by storms of different magnitudes were thencalculated for the combinations of land system andstorm regime present in the catchment. The frequencyof storms within an interval of magnitudes (Fig. 3)was multiplied by the corresponding areal landslidedensity expected from that interval (Fig. 5) , and by the proportion of the land system represented by that storm regime. Results were then summed for eachland system to calculate the average areal landslidefrequency in pasture in each land system (Table 1) .Results reflect the combined effects of inherent insta-

bility and location along the climatic gradient. For example, although Wharerata and Waihora land sys-tems show the same relation between landsliding and

storm magnitude, Waihora lands are subject toapproximately twice the areal landslide frequency of Wharerata lands because a higher proportion of theWaihora land system is located in areas characterized by high storm magnitudes. Calculated frequenciesrange between 28 slides km

2 year 1 for the Te Arai

land system and 8 slides km2 year

1 for Wharekopaelands.

For each land system, the modal value for the areallandslide frequency occurs at storm magnitudes between 180 and 320 mm and the median value at magnitudes between 220 and 360 mm. Because therecurrence interval asso ciated with these magnitudesvaries by storm regime (Fig. 3) , results were recalcu-lated for each storm regime given the distribution of land systems within each regime (Fig. 6) . The Otokoregime is characteristic of low-elevation gauges,where annual precipitation and average storm magni-tudes are relatively low. About 75% of the landslides

Fig. 6. Average areal landslide frequencies for the distribution of storm regime, land system, and vegetation present in the Waipaoacatchment. Overall average frequencies for landslides from stormssmaller than a given recurrence interval are calculated by summingvalues on each curve for the specified recurrence interval. For example, the annual average of 9.6 slides km

2 that are generated bystorms of 10-year recurrence interval or less include 3.9 under theHuanui regime, 1.6 under the Waipaoa Station regime, and so on.



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occurring within the Otoko regime are triggered bystorms with recurrence intervals of less than 45 years.The Huanui regime, in contrast, is typical of higher-

elevation gauges: high-magnitude storms occur morefrequently, and annual rainfall is about 30% greater than at Otoko. Here, the most important storms aremore frequent, and 75% of the slides occur duringstorms with recurrence intervals of less than 16 years.When results for all eight storm regimes are weighted by the proportional areal contribution of the stormregime to the catchment, 75% of the landslides withinthe catchment are found to occur during storms withrecurrence intervals of less than 27 years an d 50% at recurrence intervals of less than 8 years (Fig. 7).Although the major cyclones, such as Bola, have adramatic impact on the appearance of the landscape,they are infrequent enough that the overall influenceof such storms is less profound than that of morefrequent storms of moderate size.

These results are consistent with annual sediment yields measured for the Waipaoa catchment. Sediment yield during a year that included both a 100- and a 20-year flood was only 3.3 times as high as the averageyield during a 19-year period that included no floodswith recurrence intervals greater than 11 years (Gis- borne District Council, Gisborne, New Zealand,

unpublished data). If x represents the average sedi-ment yield for the 95% of years in which the max-imum storm has less than a 20-year recurrence

interval, the sediment yield in each of the remaining5% of years (i.e., those with floods of 20-year recurrence interval or larger) will generally be less

than or equal to 3.3 x. In a 100-year period, then, morethan 85% (=95 x/(5 3.3 x+95 x)) of the sediment yieldis expected to be produced during floods with recur-rence intervals of less than 20 years.

The relative importance of moderate-sized stormssuggests that a 40- to 60-year record of landslideactivity, conveniently equivalent to the length of theaerial photographic record at most locations, is likelyto be sufficient for characterizing the importance of landsliding in areas similar to the Waipaoa catchment.

5. Sediment delivery by landslides

The mean volumes calculated for landslides ineach land system were multiplied by the correspond-ing average areal landslide frequencies to calculate theaverage rate of sediment mobilization by landslidingin each land system. A portion of the sediment mobilized by most landslides is redeposited beforereaching a channel. The extent of redeposition wasestimated from aerial-photo observations of the dis-tribution of debris tails and from delivery ratios

measured in a similar area.Sediment delivery for landslides generated by

Cyclone Bola was estimated from delivery classesobserved on aerial photographs. For a representativeTe Arai subcatchment, 35% of the debris tails did not reach a watercourse; 40% of the debris tails traveleddown a hillslope before depositing some sediment in awatercourse; and 25% of the landslides abutted awatercourse and delivered all sediment. If partiallydelivering landslides are assumed to be randomlydistributed with respect to distance from a stream,

an average of half the sediment from this categorywould enter watercourses, and the overall sediment delivery ratio from shallow landslides would be 0.45.Measurements after three smaller storms show similar patterns of landslide distribution, and the patterns arealso similar in other land systems. Field observationssuggest that stream-side landslides may be somewhat larger than those originating farther up slopes, so theactual delivery ratio may be higher than estimated.Once in the channel system, some portion of themobilized sediment is deposited on downstream

Fig. 7. Cumulative frequency distribution for combined landslideoccurrence from all land systems and storm regimes as a function of recurrence interval.



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floodplains, decreasing the overall delivery ratio tosites farther downstream.

In comparison, at Lake Tutira, located 90 kmsouthwest of the Waipaoa catchment, an average of 68% of the landslide sediment mobilized by CycloneBola entered channels. About 12% of the mobilizedsediment was redeposited on downstream floodplains, producing a sedimen t delivery ratio of 0.56 to the lake(Page et al., 1994b) .

Delivery from the smooth hillslopes of the Tutiracatchment is expected to be more efficient than fromTe Arai hillslopes, but overbank deposition isexpected to be substantially greater at Lake Tutira because Te Arai channels are more deeply incised. Asediment delivery ratio of 0.45 to 0.68 is expected for Te Arai hillslopes in the Waipaoa catchment, and afurther 5% to 10% of the sediment is expected to belost to overbank deposition. Consequently, a sediment delivery ratio of 0.5 is assumed on all land systems inthe Waipaoa catchment for further calculations.

Applying the estimated sediment delivery ratio tothe average rate of sediment mobilization by land-slides in each land system provides an estimate of sediment delivery from landslides on pasture lands ineach system (Table 2) .

6. Rates of landsliding in forests

Measurements in forest and scrub show lower areallandslide densities than in pasture for equivalent storm

magnitudes (Fig. 5). Although the area sampled inforest and scrub represents only 1.4% of the total areaof the studied land systems, results provide a basis for general comparisons and are consistent with those of studies in similar areas.

Measurements from primary forests of the Whar-erata and Waingaromia land systems, scrub lands of the Waihora system, and partially cut forest on Mako-mako and Wharekopae systems were compared with

values predicted fo r past ure in t hose areas using therelations shown in Fig. 5 (Fig. 8) . Results suggest that

Table 2Contribution by landslides in each land system to the sediment load of the Waipaoa River at Kanakanaia

Catchment area Average landslide sediment delivery (1000 t year 1) from Percent of suspended

above Kanakanaia(km2) Pasture Forest or scrub

b sediment load at Kanakanaia a

Te Arai 250 555 46 6.3Waingaromia 26 8 12 0.2Makomako 131 87 15 1.1Waihora 40 62 4 0.7Wharerata 207 284 48 3.5Wharekopae 437 163 13 1.8Others 372 96 34 1.4

Total 1462 1253 171 15a The suspended sediment yield of the Waipaoa River at Kanakanaia averaged 9.5 106 t year

1 between 1972 and 1993 with a 95%confidence interval of 7.0 106 to 13 106 t year

1. The range of percentages indicated in this column is calculated using the bounds of theconfidence interval.

b Combined area of exotic forest, indigenous forest, and scrub was measured from 1995 imagery.

Fig. 8. Ratio of areal landslide densities observed in forest and scrubto those expected in pasture for storms of different sizes.



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sediment in the Waipaoa River if the Waipaoa sedi-ment yield is assumed to be 7500 t km

2 year 1,

as estimated for the Matawhero gauge site. If 50%

(221 km2

) of the remaining pasture is converted in themost landslide-prone land system, the Te Arai, Wai- paoa sediment loads may decrease by an additional4%. Conversion of pasture to forest on less erodibleland systems will have a correspondingly smaller effect. Even if all the remaining landslide-prone pasture outside of the Te Arai system is converted(689 km 2), for example, the resulting change in land-sliding rate would reduce Waipaoa sediment loads byonly 4%.

A more efficient approach to reforestation wouldtarget the most unsta ble land systems in the most erosive storm regimes (Table 3) . Using this approach,reforestation of the 66 km 2 currently in pastu re in themost susceptible areas (shown in bold in Table 3)would reduce the input of sediment from landslides by20% and decrease Waipaoa suspended sediment loads by about 3%. If the landslide reduction efficiencyof a reforestation plan is described by the change insediment input from landslides per unit area refor-ested, the efficiencies of a prioritization strategy can be compared to those for a strategy of randomselection (Fig. 9) . For example, a 40% reduction in

landslide-derived sediment could be achieved throughreforestation of 8% of the Waipaoa catchment if landsare appropriately prioritized, whereas random selec-

tion of lands would require that 25% of the catchment be converted to achieve the same decrease in sediment load (Fig. 9) . Prioritization in this case would provide

three times the efficiency of a random strategy.

9. Evaluation of potential errors

The results described above rely on multiple datasources and on a lengthy sequence of calculations.Each step in the analysis introduces some level of uncertainty. Given the complexity of the analysis, it isimportant to determine how reliable the reportedresults are likely to be. The diversity of methods used,however, prevents a standard calculation of confi-dence intervals for results: uncertainties in mappingare not readily compared with uncertainties in inte-gration of probability curves or with confidenceintervals for measurements of bulk density. Instead,reliability was tested using two methods of sensitivityanalysis.

The sensitivity of each major conclusion was first evaluated independently for each s ource of uncer-tainty and each major assumption (Table 4) . Eachresult was recalculated to incorporate an introducederror that represents either the 95% confidence inter-

val for an input variable, the estimated maximumlikely error, or complete removal of the input variablefrom consideration. In the case of storm regimes, thelevel of detail needed in future analyses was explored by testing results both for the likely maximum poten-tial error and for removal of the input variable.

Both the estimate of recurrence interval for thedominant landslide-generating storms and the estimateof the minimum proportion of the area that could bereforested to achieve a 40% decrease in landslidesediment change little with most sources of introduced

error. These results reflect calculated proportions, anderrors that affect the numerator and denominator equally do not affect the result. In contrast, thecalculated total and proportional inputs of sediment from landslides are directly proportional to deliveryratio and to the average volume of landslides, andresults are found to be most sensitive to potentialerrors in these factors. The proportional input can also be strongly influenced by errors in the estimatedsediment load of the Waipaoa River. Other sourcesof error, including those associated with definition of

Fig. 9. Percentage change in landslide-derived sediment for different levels of reforestation under two strategies for prioritizing re-forestation sites.



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relationships between storm magnitudes and landslid-ing, would cause less than a 20% change in thereported results.

Because long-term rainfall records and high den-

sities of rain gauges are rarely available for landslide- prone areas, the sensitivity of results to definition of storm regimes was evaluated at several levels. Simplemisclassification of 20% of the land introduced errorsthat are consistently less than 10%. However, whencalculations are carried out assuming a single stormregime, errors of 48% to 80% are introduced. Divid-ing the area into an upland regime and a lowlandregime removes most the error. This pattern suggeststhat calculations such as those carried out for theWaipaoa catchment rely on accurate characterization

of major variations of rainfall regime within thecatchment, but that gradients within the major cate-gories are of substantially lesser importance.

Table 4 indicates potential errors introduced by

each source of uncertainty in isolation. In reality,errors are introduced simultaneously from multiplesources. A Monte Carlo simulation similar to that used in Generalized Likelihood Uncertainty Estima-tion (Beven and Freer, 2001) was carried out toevaluate the potential importance of combined errors.Errors for 32 variables (e.g., slopes for five relations between areal landslide density and storm magnitude,mean landslide volumes for six land systems, etc.)were assumed to be normally distributed, with stand-ard deviation estimated directly or from the range of

Table 4Sensitivity of reported results (bottom row) to modifications of input variables

Source of uncertainty Modification tested Error Change in principal conclusions b

type a

(1) Landslidesediment b (2) Landslide proportion b (3) Stormrecurrence b (4) Areato reforest b

Slide storm relations (percentage change from reported result)Slope F 95% CI 1 F 15 F 16 0 3.7 to 2.4Intercept unconstrained c 3 1.9 9.9 0 14Categories three classes, not four d 2 7.8 11.1 5.6 6.1Other land types F 100% e 3 6.1 to 4.1 9.1 to 6.2 0 0

Storm regime curves one regime f 3 48 62 80 64two regimes f 2 6.5 8.4 16 17

Storm regime map 20% misclassified g 2 1.7 9.4 1.6 2.4Land system map 20% misclassified g 2 0.4 8.9 1.6 0.6Mean slide volume F 25% 2 F 25 F 25 0 0Delivery ratio 0.35 to 0.63 2 30 to 26 10 to 19 0 0Soil bulk density F 95% CI 1 F 2.0 F 2.0 0 0Landslide rate in forest 10% of pasture 2 4.9 6.0 0 8.2

40% of pasture 2 9.7 12 0 16Waipaoa sediment load F 95% CI 1 0 21 to 28 0 0

Reported result (no changes) 2.6 106 t year 1 0.15 27 years 0.08

Introduced errors represent either 95% confidence intervals, maximum potential errors, or removal of the factor from consideration. Sensitivityis expressed as a percentage change from the reported result. Differences more than 20% from that reported are shown in italic font; those between 10% and 20% of that reported are shown in bold font.

a Type of error introduced: (1) Bounds of 95% confidence interval; (2) estimated maximum potential error; (3) removal of factor fromconsideration.

b Conclusion tested: (1) Total sediment input at Kanakanaia for which landslides are responsible; (2) proportion of sediment yield at Kanakanaia for which landslides are responsible; (3) recurrence interval for storms larger than those generating 75% of landslides; (4) minimum proportion of area that can be reforested to reduce landslides by 40%.

c All regressions but that for Wharakopae are recalculated without constraining the intercept by observations of the threshold storm size for landsliding. A threshold of 100 mm is assumed for Wharakopae because available climatic data are for storms greater than 100 mm.

d Data from Makomako, Waihora, Wharerata, and Waingaromia are pooled.e Input is first considered 0 from other lands, then as twice the rate of Wharekopae lands.f Storm data are pooled and used to construct a single frequency curve, then two curves.g Twenty percent of each map unit is reassigned in equal parts to the other units.



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maximum likely error for each variable; map mis-classifications and errors in storm regimes were not considered. Results were calculated 100 times, eachtime with errors randomly generated from each of the32 estimated error distributions. Confidence intervalswere then calculated from the standard deviations of

the simulated sediment yields, producing an estimated95% confidence interval of 2.6 106F 0.6 t year 1 for the sediment yield from landslides above Kanakanaia.The percentage input from slides at Kanakanaia isestimated to be 15% F 5% using the same method, andthe minimum percentage of the area that can bereforested to achieve a 40% decrease in landslidesediment input is estimated to be 8.3% F 1.5%.

Because the Te Arai land system produces most of the landslide-related sediment, results are found to bemost sensitive to errors associated with that system.

As expected from the sensitivity analysis for individ-ual variables, potential errors in the average volume of landslides in the Te Arai system (Fig. 10B) exhibit themost influential effect, explaining 57% of the totalsimulated variance.

10. Conclusions

Where a process regime is subject to extremelylarge events, it is not possible to interpret data fromshort-term records unless the relative importance of large events is understood. An analytical approachwas developed that allows short-term records of thedistribution of landslides to be used in conjunctionwith long-term climatic records to allow large eventsto be appropriately represented in calculations of

Fig. 10. Variability of modeled sediment input from landslides as calculated to incorporate uncertainty in 32 variables, with errors selectedrandomly according to their assumed distributions. Results are displayed as functions of four variables from the Te Arai land system. Scatter inthe y-dimension represents the combined influence of errors in the 32 variables; the randomly generated values for each of four variables amongthe 32 are plotted along the x-axes.



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average rates of landsliding. Such an approach pro-duces results independent of weather patterns duringthe observation interval, thereby providing a basis for

evaluating the effects of hypothetical changes in landuse or climatic conditions.The calculations are based on relationships

between areal landslide densities and the magnitudesof the storms that triggered the slides. Any suchrelation is necessarily simplistic because it does not account for the antecedent precipitation, seasonaldifferences in erodibility, influences of previousevents on erosion resistance, or a variety of other potential influences. Results for the Waipaoa catch-ment, however, indicate that these complexities areminor compared to the influence of storm magnitude,which alone accounts for 65% to 90% of the variancein the relationships once differences in land systemand vegetation are accounted for. In general, largestorms at deforested sites on erodible slopes produce alarge effect, irrespective of other influences. Secon-dary influences such as antecedent precipitation, how-ever, may become important for individual storms.Consequently, the measured relations are more con-fidently used to estimate long-term averages than to predict the specific inputs from a particular storm.

In the present study, results are used to assess the

likely influence of reforestation on sediment loads in amajor river. Reported results are necessarily approx-imate because of uncertainties in such quantities asestimated delivery ratios for landslides, extent of overbank deposition, and average sediment yield for theWaipaoa River. But despite these uncertainties, broad patterns of influence are strongly established. First,most landsliding is triggered by storms of moderaterecurrence interval. Second, a small portion of thelandscape produces a large portion of the landslide-derived sediment, so prioritization of the most suscep-

tible areas for reforestation is a useful strategy for increasing the efficiency of erosion-control plans. With prioritization, a 40% reduction in sediment input fromlandsliding could be achieved through reforestation of about 8% of the Waipaoa catchment. Without prioriti-zation, a 40% reduction would require reforestation of 25% of the catchment. A 40% reduction in landslideinputs, however, would decrease the sediment load of the Waipaoa by only about 6%. Clearly, a viable sedi-ment control plan for the catchment requires consid-eration of multiple sediment sources.

An event-based predictor for the frequencies of landslides can be used for a variety of other applica-tions as well. An understanding of the dominant

forces that sculpt a landscape requires an understand-ing of the relative effectiveness of events of different magnitudes and frequencies. Such information is particularly important as a basis for interpreting theHolocene stratigraphic record. In addition, land man-agers are better able to make effective land-usedecisions if they understand the likely effects of different kinds of storms and know how frequentlythose events might occur. If large events are veryimportant but infrequent, it is all too easy to becomecomplacent about the apparent success of soil con-servation measures that have never been tested by alarge storm. Conversely, if large storms are dramatic but of little long-term consequence, management strategies that focus on controlling sediment frommore mundaneand more manageableevents will provide the most useful and cost-effective results.

Acknowledgements

We thank Ian Lynn, Noel Trustrum and TerryCrippen for assistance and discussions in the field,and Jack Lewis for statistical advice. John Dymond,Paul Luckman, Mike Crozier, Robert Ziemer, and ananonymous reviewer provided helpful comments onthe manuscript. Funds for this research were provided by The Foundation for Research, Science andTechnology under contract number C09612.

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