Modelling the formation of residual dune ridges behind ... · RDRs measured in the Lagoa Azul transect (no. 6 in Fig. 3 and in Table 2). (C) Flat and wide RDRs in the Lagoa Azul proﬁle

Modelling the formation of residual dune ridges behind barchandunes in North-east Brazil

NOAM LEVIN*, HAIM TSOAR� , HANS JURGEN HERRMANN� ,§, LUIS P. MAIA– andVANDA CLAUDINO-SALES***Department of Geography, The Hebrew University of Jerusalem, Mount Scopus, Jerusalem 91905, Israel(E-mail: [email protected])�Department of Geography and Environmental Development, Ben-Gurion University of the Negev, BeerSheva 84105, Israel�The Swiss Federal Institute of Technology Zurich, Computational Physics, ETH-Honggerberg, Institutfur Baustoffe (IfB), HIF E 12, Schafmattstr. 6, 8093 Zurich, Switzerland§Departamento de Fısica, Universidade Federal do Ceara, 60451-970 Fortaleza, Brazil–Instituto de Ciencias do Mar - LABOMAR, Av. Abolicao, 3207, Meireles, Fortaleza, Ceara, Brazil**Departamento de Geografia, Universidade Federal do Ceara, 60451-970 Fortaleza, Ceara, Brazil

Associate Editor: Charlie Bristow

ABSTRACT

Residual dune ridges are often formed by vegetation growing along a line some

distance upwind of the lower stoss slope of migrating dunes. This process is

common in areas where vegetation germinates along the edge of thewater during

the rainy period when the water level is higher and interdune areas are flooded.

The phenomenon occurs on a large scale in North-east Brazil, because of the rise

and fall in groundwater level at the end of the rainy season. Each residual dune

ridge corresponds to the position of the dune during the wet period in each year.

Therefore, variations in the distance between these residual dune ridges could be

used potentially to monitor climatic fluctuations in rainfall and wind. To

examine the potential use of these residual dune ridges for the reconstruction of

past climatic fluctuations, amodel that simulates them under varying conditions

of wind, rainfall and evaporation rates was formulated. Themodel was tested for

sensitivity to climatic variability in North-east Brazil and validated against

residual dune ridge displacements asmeasured in the field and from high spatial

resolution satellite images. Based on the results, it is concluded that residual

dune ridges may not form in North-east Brazil in years which are exceptionally

dry, as may happen during El-Nino events. When this type of event happens, the

distance between adjacent residual dune ridges corresponds to more than one

year and, therefore, the correlation betweendunedisplacements andwindpower

becomes weak or even disappears. Additionally, because of biotic, aeolian and

hydrological processes, these arcuate residual dune ridgesmaynot preserve their

initial shape for long periods. The presence of residual dune ridges testifies to the

temporary floodingwhichmayormaynot be seasonal.However, thepotential for

using residual dune ridges to reconstruct the palaeo-climate of wind regime on a

yearly basis or to identify past El-Nino events seems to be limited.

Keywords Coastal dunes, model, rainfall, residual dune ridges, wind.

INTRODUCTION

Reconstructing past climate fluctuations frompalaeo-climate proxy data is important for detec-

tion of anthropogenic climate change (von Storchet al., 2004). A range of geomorphological effectsof decadal to century-scale oscillations has beenstudied in the past, with dune activity being one

Sedimentology (2009) doi: 10.1111/j.1365-3091.2009.01048.x

� 2009 The Authors. Journal compilation � 2009 International Association of Sedimentologists 1

of them (Viles & Goudie, 2003). The spacingbetween residual dune ridges in North-easternBrazil, which was thoroughly investigated in thisstudy, has been suggested by Maia et al. (2005) asa possible proxy for El-Nino Southern Oscillation.Residual dune ridges are known to form by

vegetation growing along a line some distance upthe lower stoss slope of dunes (Claudino-Sales &Peulvast, 2002). This morphological responsehappens during the rainy period when the waterlevel is higher (and interdune areas are flooded)and vegetation germinates along the edge of thewater. Arcuate dune ridges of this type are knownfrom many areas in the world and have beengiven different names by different authors. InBrazil, they are called ‘crescent-shaped semi-circular residual hillocks’ by Claudino-Sales &Peulvast (2002) or ‘low vegetation dunes/marks’,‘cuspidate marks’ or ‘sinuous dune marks’ byMaia et al. (2005). In this paper, the term ‘residualdune ridges’ (RDRs) is used. Two different pro-cesses have been proposed to form dune ridgesthat have a similar appearance. The differencesbetween the two processes are related to the windregime (unidirectional or bi-directional) andwhether the dune ridges are formed by risingwater levels or counter winds:

1 In dune areas where the wind is almost uni-directional throughout the year, as in NE Brazil oralong the coast of Queensland (Pye, 1982), thedevelopment of these RDRs was described asfollows by Jimenez et al. (1999; Fig. 1): during thewet season, high rainfall reduces aeolian trans-port rates and, consequently, dune mobility. Inaddition, the formation of interdune ponds pro-motes vegetation growth at the base of the dunebecause of both an increase in the humidity of thesand and also the drop in wind intensity at thebase of the dunes. This increase in sand stabilityresults in a temporary fixing of the dune upwindbase by plant growth. During the dry season,wind intensity increases, sand humidity de-creases and, consequently, wind becomes moreefficient in transporting sediment, resulting in thefree migration of the dunes. However, the vege-tated part at the base of the dune is stabilized,leaving an arcuate RDR as the dune advances.2 For dunes located in Friesland (in the

Northern Netherlands), Van Dieren (1934) namedthese ridges ‘gegenwalle’ (i.e. counter ridges). Thedevelopment of plants of the gegenwalle ridges inthe area described by Paul (1944; the CuronianSpit of Lithuania) takes three years before vege-tation is established and becomes fully perma-

nent. The drift potential of sand by the wind (DP;Fryberger & Dean, 1979) in that area is very high(DP = 2028; based on table 5 in Paul, 1944).However, the wind regime there is multidirec-tional and the ratio between the resultant driftpotential (RDP) and DP is 0Æ08. The gegenwalleridges present there are formed by easterly‘counter’ winds blowing in winter back down thedune fields against the dominant westerly wind,transporting sand off the dune and into the lowresidual ridge where plants are beginning toestablish.

Arcuate RDRs are present on a large spatialscale in the coastal dunes of NE Brazil (Fig. 2),because of the seasonal rise and fall in ground-water level during the wet and dry seasons in thistropical climate, where annual rainfall rangesbetween 1000 and 2000 mm (Dominguez & Bitten-court, 1994; Jimenez et al., 1999; Claudino-Sales& Peulvast, 2002; Meireles & Serra, 2002; Barbosa& Dominguez, 2004). However, similar RDRs havebeen observed also in desert dunes because ofinundation during fluvial flood events (in theUSA: Langford, 1989; in Tunisia: Purvis, 1991), orbecause of inundation by sea water from lagoonsduring the high tide (in Baja California, Mexico:Inman et al., 1966).Large variations in the distance between RDRs

may reflect interannual variability in the rainfalland/or wind intensity and could potentially beused to monitor short-term (annual and decadal)climatic fluctuations in areas where these RDRsare preserved. Dune displacement distanceshave been extracted accordingly from suchRDRs by Jimenez et al. (1999), whereas Maiaet al. (2005) suggested a weak but significantcorrelation between the yearly displacement of abarchan dune and the Southern OscillationIndex (RSpearman )0Æ383; P < 0Æ05, between theyears 1966 and 1995).

Factors affecting dune movement

Understanding the factors affecting dune mobilityis essential for modelling the formation of RDRs.Indices of sand mobility traditionally are relatedto precipitation, evaporation and wind magnitude(Lancaster, 1997). Several studies identify windregime and wind power as the most importantphysical factors in determining the mobility ofdunes (Fryberger & Dean, 1979; Tsoar, 2005). Thewind parameters to be considered are windvelocity (above the threshold required to keepsand in saltation) and directionality.

2 N. Levin et al.

� 2009 The Authors. Journal compilation � 2009 International Association of Sedimentologists, Sedimentology

As sand mobility is a function of wind power(related to the cube of the wind speed above thethreshold speed; Bagnold, 1941; Kawamura,1951), the drift potential of the sand by the windcan be estimated by applying the method devel-oped by Fryberger & Dean (1979), using theindices of DP and RDP (Fryberger & Dean, 1979).The effect of rainfall on sand movement is not

straightforward. It is well-known that when sanddunes are wetted by rainfall, the high moisturecontent of the sand inhibits sand movement.However, quantitative estimations of the effect ofsand moisture on the decrease of its movementvary (as reviewed by: Namikas & Sherman, 1995;Cornelis & Gabriels, 2003; Wiggs et al., 2004).Dune activity may continue even when most of

the dune is wetted by rainfall. As the wind driesthe upper layer of sand grains, the grains becomesusceptible to entrainment and, once entrained,they expose the moist layer of sand underneaththem (Jackson & Nordstrom, 1997). In a studyconsidering a remobilized parabolic dune in theNetherlands, activity of the dune was influencedstrongly by precipitation that slowed the migra-tion rate (Arens et al., 2004). However, theimportance of rainfall as a factor inhibiting dunemovement may change between different climateregions and, in the coastal dunes of Israel, norelationship was found between rainfall and sandmobility (Levin et al., 2006).To understand better the formation of RDRs

and to examine their potential use for the

A

B

C

D

Fig. 1. Schematic developmentof residual dune ridges (RDRs).(A) Dune movement during the dryseason. (B) Rising water level duringthe wet season. (C) As the waterlevel gradually drops down and thedune moves ahead, a RDR startsforming behind as sand is retainedby plants and moisture. (D) Free-moving dune in the dry season witha RDR left in its wake. The size ofthe arrow indicates respective windpower during each period. The sizeof the RDR in this figure is exagger-ated with respect to the dune size.

Modelling dune ridges behind barchan dunes in NE Brazil 3


A B

C D

E F

Fig. 2. Photographs showing residual dune ridges (RDRs) in NE Brazil; (A) to (E) taken by NL, (F) taken by HH.(A) Establishment of herbaceous plants (mainly Cyperus maritimus) on the base of the dune following the lowering ofgroundwater level. The height of the C. maritimus plants in the photograph is up to 10 to 20 cm. (B) A sequence of theRDRs measured in the Lagoa Azul transect (no. 6 in Fig. 3 and in Table 2). (C) Flat and wide RDRs in the Lagoa Azulprofile (no. 5 in Fig. 3 and in Table 2). The average spacing between RDRs in photographs (B) and (C) is 15 m.(D) Development of large bushes on RDRs in the deflation area of transects no. 3 and no. 4 (shown in Fig. 3 and inTable 2). The average spacing between RDRs in this photograph is 25 m (E) Dense vegetation of trees and large bushesdeveloped on the mature RDRs about 1Æ5 km south-west of Mandacaru (Fig. 3). The width of the non-vegetated areabetween the two RDRs in this photograph is about 10 m. (F) Aerial photograph showing partly flooded RDRs betweentwo dunes in the Lencois Maranhenses dune field. The spacing between adjacent RDRs in this photograph is between10 and 15 m.

4 N. Levin et al.


reconstruction of the fluctuation in climate dur-ing the 19th and 20th Centuries, a quantitativemodel was devised to simulate them, undervarying wind, rainfall and evaporation rates. Themodel was tested for sensitivity to climaticvariability within NE Brazil and validatedagainst actual dune displacements, as measuredfrom high spatial resolution satellite images andin the field.

METHODS AND DATA SOURCES

Study area

The study area is located within the north-easterntropical coast of Brazil in the states of Maranhaoand Ceara (Fig. 3). Almost the entire Ceara coast(about 570 km long), as well as that of Piauı andthe eastern part of that of Maranhao are backed byextensive dune fields (the largest dune field beingthe Lencois Maranhenses, encompassing roughly1000 km2). The RDRs that are the focus of thisstudy are common phenomena in many of thesedune fields. The RDRs are apparent mostly withinbarchan dune fields (as in Jericoacoara) or ondeflation plains over which the dunes havemigrated (as in the Pequenos Lencois or in theeastern part of the Lencois Maranhenses; Fig. 3B).The current active dunes (Figs 2 and 3) penetratesome 5 to 10 km inland (in Maranhao even morethan 20 km) downwind of the coastline andcomprise barchans, barchanoids and sand sheets,with the dominant dune type depending on theavailable sand stock. At present, the active dunesare separated from the coast by a deflation plain600 to 2000 m wide and are migrating on top ofolder generations of dunes. The migration rate ofthe barchans of Jericoacoara is estimated to be17Æ5 m year)1 on average (Jimenez et al., 1999).

Climate of North-eastern Brazil

The wind climate of north-eastern Brazil isgoverned by the easterly strong trade winds.Seasonal latitudinal positioning of the Inter-Tropical Convergence Zone (ITCZ) determinesboth the incidence of dominant winds and rain-fall regimes (Wang et al., 2004). Previous palaeo-climatic studies have found that over the past210 000 years wetter periods in tropical North-eastern Brazil may be explained by a southwarddisplacement of the ITCZ (Wang et al., 2004). Thepresent study deals with the effects of the latitu-dinal position of the ITCZ on geomorphological

features of coastal dune fields in NE Brazil on ashorter time scale of dozens to hundreds of years.The annual average rainfall in Fortaleza (Fig. 3A)is 1663 mm (for the years 1974 to 1995) and ishighly seasonal, with a wet period from Januaryto July, when almost 93% of the rainfall occurs(Jimenez et al., 1999). Rainfall increases west-ward, where at the Lencois Maranhenses dunefield (Fig. 3) it is more than 2000 mm per year.During the dry period from August to Decemberthere is almost no rainfall and wind velocity ismuch higher than in the wet season. The windpower increases from Maceio (in the state ofAlagoas, east of the study area) to Aranau (in thestate of Ceara), decreasing dramatically in SaoLuis and westward (Levin et al., 2007). The windpower values at Aranau, Pecem and Parajurucorrespond to values found within areas withhighly active dune systems (Tsoar, 2005; Levinet al., 2007; see the values below).

Climatic time series

As a result of the paucity of recorded meteoro-logical data spanning the past 60 years in NEBrazil, most of the climatic data used were basedon gridded models such as the NCEP/NCARReanalysis Project at the NOAA-CIRES ClimateDiagnostics Center (NCEP, 2007). As the type ofcoastal dunes studied here covers large areasextending between 43�19¢W and 40�24¢W (Fig. 3),their spatial scale is similar to that of the climaticdata which was derived mostly from griddedmodels at spatial resolutions between 0Æ5� and2Æ5�. Almost all of the climatic time series thatwere used were downloaded from the WorldWide Web (Table 1). The following is a shortdescription of these data sets, according to thedifferent climatic variables.

WindFor the calculation of the indices of DP and RDP(Fryberger & Dean, 1979), both wind speed andwind direction are needed. These parameters areprovided usually either as tables showing therelative per cent time for different wind speedcategories from different directions (as in Fryber-ger & Dean, 1979) or as detailed time series fromwhich such tables are constructed. Actual mea-surements of both wind speed and wind directionfor the study area were available only from theairport of Fortaleza, Ceara (which is located13 km from the coastline), at varying temporalresolutions, from January 1974 onwards (Table 1).However, as these wind data were available for



only one location and were not detailed before1998, they were not used. Rather, synthetic windspeed data from the NCEP/NCAR ReanalysisProject at the NOAA-CIRES Climate DiagnosticsCenter were used (NCEP, 2007). These data fullycover the time frame between January 1948 andDecember 2005, 58 years altogether, at a temporal

resolution of every 6 h and at a spatial resolutionof 2Æ5�. Within the NCEP/NCAR ReanalysisProject, the variables of ‘u-wind’ (east/west windcomponent with east being positive) and ‘v-wind’(north/south wind component, with north beingpositive) belong to category A (Kalnay et al.,1996), which indicates that the analysis variable

A

B

Fig. 3. (A) Map of the study area showing the locations of the NCEP/NCAR Reanalysis grid points that were used inthe model for time series of wind, potential evaporation and rainfall. Validation areas where satellite images, aerialphotographs and field work were used were located in Jericoacoara and in the Lencois Maranhenses coastal dunefields. (B) Map of the field sites where transects of residual dune ridges were measured in the field in October 2006.The transect numbers relate to Table 2.

6 N. Levin et al.


Table

1.

Climatictimeseries.

Climatic

variable

Start

date

Enddate

Completeness

Source

Location

Temporal

resolution

Inputin

model?

CorrelationwithFort-

alezarainfall

1948to

2005

Monthly

Yearly

Rainfall

January

1849

December

2004

99%

http://dss.ucar.edu/datasets/

ds570.0/

Fortaleza(station

823970)

Monthly

Yes

––

January

1974

December

2004

94%

http://dss.ucar.edu/datasets/

ds570.0/

SaoLuiz

(station

822800)

Monthly

No

0Æ74**

0Æ70**

January

1974

December

2005

47%–100%

http://w

ww.funceme.br/

DEPAM/index.htm

Variousstations

alongthe

coast

ofCeara;Fig.3

Daily

No

0Æ73**

to0Æ95**

0Æ70**

to0Æ95**

January

1951

December

2000

100%

http://w

ww.dwd.de/

en/FundE/

Klima/

KLIS/int/GPCC/

Every

0Æ5�

Monthly

Yes

0Æ84**

to0Æ86**

0Æ84**

to0Æ85**

Windsp

eed

anddirection

01/01/1974

19/09/1998

99%

FUNCEME

FortalezaAirport

3timesdaily

(12,18,24)

No

)0Æ67**

)0Æ45*

14/08/1999

01/02/2002

99%

Half-hourly

No

)0Æ70**

–

06/05/2003

20/04/2006

100%

Hourly

No

)0Æ80**

–

12/02/2006

03/04/2006

75%

http://w

ww.eere.energy.gov/

buildings/

energyplus/cfm

/weatherdata/

weather_request.cfm

FortalezaAirport

Hourly

No

)0Æ78**

–

RDP

01/01/1948

01/05/2006

100%

Calculatedfrom

u-w

ind&

v-w

inddownloaded

from

http://

www.cdc.noaa.gov/

cdc/reanalysis/

reanalysis.sh

tml

Every

2Æ5�

Monthly

based

on4

timesdaily

(6,12,18,24)

Yes

)0Æ52**

to)0Æ67**

)0Æ20

to)0Æ45**

Potential

evaporation

January

1948

April2006

100%

http://w

ww.cdc.noaa.gov/

cdc/reanalysis/

reanalysis.sh

tml

Every

2Æ5�

Monthly

Yes

)0Æ43**

to)0Æ69**

)0Æ20

to)0Æ37**

*P<0Æ05;**P<0Æ001.

RDP,resu

ltantdriftpotentialofsandbywind.



is influenced strongly by observed data and,hence, it is in the most reliable class. Based onthe NCEP/NCAR variables of u-wind and v-windat 10 m, wind speed and wind direction werecomputed for each time step (i.e. every 6 h),based on which the monthly values of DP andRDP were derived for the period between 1948and 2005, following Fryberger & Dean (1979).

RainfallThe city of Fortaleza, Ceara, has one of the longestrecords of monthly time series of rainfall fora tropical station, starting in January 1849(Table 1). Time series for other stations in NEBrazil do not cover such long periods and aremostly available from 1974 onwards. To achieve afull temporal cover of rainfall data a new griddedmonthly precipitation data set was used, coveringthe period from 1951 to 2000 for all global landareas with a spatial grid resolution of 0Æ5� · 0Æ5�(Beck et al., 2005). This data set was developedon the basis of the most comprehensive databaseof monthly observed precipitation data world-wide (Global Precipitation Climatology Centre).Rainfall data for the years 1948 to 1950 and 2001to 2005, which were not covered by the griddedrainfall of Beck et al. (2005), were computedbased on linear regression with the Fortalezarainfall time series (which had full data). Thecorrelation coefficient (R) between the variousgridded time series of rainfall (Beck et al., 2005)and that of Fortaleza ranged from 0Æ84 to 0Æ86 (forthe years 1951 to 2000).

Potential evaporation ratePotential evaporation rates were derived from theNCEP/NCAR Reanalysis Project at the NOAA-CIRES Climate Diagnostics Center (NCEP, 2007).These data fully cover the time frame betweenJanuary 1948 and December 2005 (58 years) andwere downloaded at a monthly temporal resolu-tion, at a spatial resolution of 2Æ5�, in units ofW m)2. Within the NCEP/NCAR Reanalysis Pro-ject the variable of potential evaporation ratebelongs to category C, which indicates that thisvariable is derived solely from the model fields(Kalnay et al., 1996). Although not based ondirect observations, Kalnay et al. (1996) note thatthere is little evidence of any long-term drift (i.e.errors) in global averages of potential evaporationvalues in the NCEP/NCAR Reanalysis (indicatingthat potential evaporation, as derived from theNCEP/NCAR, is quite reliable). To convert theabove potential evaporation rates (W m)2) into anequivalent evapotranspiration rate in units of

millimetres per day, values were multiplied by afactor of 0Æ0353. This factor equals the number ofseconds in a day (86 400), divided by the value of2Æ45 · 106 J kg)1 (at 20�C), whereby a density ofwater of 1000 kg m)3 was assumed (following Boset al., 2002).

Model development

In the development of the model, the followingassumptions were used:

1 Sand movement is a function of wind speedalone.2 The threshold wind velocity Ut for sand

movement, measured at an elevation of 10 m is6 m sec)1 (ca 12 knots as used by Fryberger &Dean, 1979 and by Tsoar, 2005).3 The dunes are moving over a flat surface.4 The sand lost from the dunes to form the

RDRs is negligible with respect to the size of thedunes and, therefore, the dunes maintain theirshape and height and do not increase theirvelocity with time.5 The formation of RDRs is a function of rainfall

contribution to the groundwater. Infiltration insand is relatively very high (the hydraulic con-ductivity at saturation for sand dunes is veryhigh, between 10)3 and 10)4 m sec)1; Tsoar,1990). The actual evaporation from dune sand isrelatively low (Tsoar, 1990). Hence, evaporationis not so effective in moisture loss from the sanddunes.6 Spatial homogeneity of all input variables

(rainfall, wind and potential evaporation) withinthe dune fields for each of the model runs.7 Water is lost from interdune ponds only due

to evaporation and not as a consequence of localephemeral rivers, percolation or groundwater.8 It was assumed that the RDRs remain un-

changed once they are formed. Therefore, processesrelated to subsequent growth or deterioration ofthese RDRs caused by vegetation cover, sedimen-tation or erosion by wind or by water, grazing ortrampling (as is common in nebkha dunes; Teng-berg, 1995; Tengberg & Chen, 1998; Dougill & Tho-mas, 2002)werenot included in themodel, to avoidadditional factors in the model.

The temporal resolution at which the modelwas built was set to one month, corresponding tothe highest temporal resolution available forrainfall data and the time frame covered by theNCEP/NCAR Reanalysis Project at the NOAA-CIRES Climate Diagnostics Center (NCEP, 2007):between January 1948 and December 2005,

8 N. Levin et al.


58 years altogether (Table 1). The model itselfconsists of two sections.

The dune movement sectionIn this section, the input is the time series ofmonthly resultant drift potential values. Resul-tant drift potential values were then transformedinto rates of sand transport using (followingFryberger & Dean, 1979, substituting DP by RDPas they are highly correlated in the study areabecause of the unidirectional wind regime):

Q ¼ F � RDP ð1Þ

where Q represents the sand transport rate(expressed in units of m3 m-width)1 year)1) andF represents a constant conversion factor. Fol-lowing preliminary runs of the model withdifferent values of F ranging from 0Æ01 to 0Æ13, itwas found that for this factor a value of 0Æ05 gavethe best approximation of annual dune movementrates as measured in the field, with root meansquared differences of less than 10 m. This valueof F corresponds to a threshold shear velocity ofabout 18 cm sec)1 (compared with thresholdvelocities of 16 to 19 cm sec)1 presumed byBullard, 1997). Calculating the threshold shearvelocity using the Bagnold (1936) equation (eq. 6in Sherman et al., 1998) and a median graindiameter of 0Æ25 mm results in a value16 cm sec)1. As grain diameter size changeswithin dune fields (with distance from the coast-line) and between dune fields (see Levin et al.,2007), it was preferred to tune the conversionfactor to make the model fit better a priori.The following modification of the equation

used by Jimenez et al. (1999, eq. 1), was appliedto transform the rates of sand transport intomigration rates (m year)1):

m ¼ Q � L �W

Vð2Þ

where Q is the aggregated (bulk) aeolian transportrate per unit width, V is the total sand volume ofthe dune, L/m is the required time for a dune oflength L to migrate at a rate of m, a distance equalto its total length, and W is the dune width. Anempirical relationship was developed betweenthe volume, width, length and movement rate forbarchan dunes in Jericoacoara and Lencois Mar-anhenses based on Jimenez et al. (1999; figs 8and 9). The output of this section of the model wasa monthly time series of the position x(t) of thestoss side of the dune along its movement axis:

xðtÞ ¼ xðt � 1Þ þmðtÞ ð3Þ

where x(t) presents the position of the stoss sideof the dune along its movement axis, x(t ) 1)presents the position of the stoss side of the dunein the previous month and m(t) presents dunemigration in that month (based on Eq. 2).

The RDR height sectionIn this section, the input is the time series ofmonthly rainfall and evaporation values. Eachmonth, at the horizontal location determined bythe dune movement section, if there was morerainfall than potential evaporation, groundwaterlevel was assumed to rise corresponding to thedifference between rainfall and potential evapo-ration. In months when potential evaporation wasgreater than rainfall and groundwater level wasalready >0, the water level height would decreaseaccording to the difference between potentialevaporation and rainfall. It was assumed thatthe height of the dune ridge corresponds to themaximum height of the groundwater tablereached in that year, because of the formation ofa dune crust on the wet dune base which is sooncolonized by coastal vegetation (Claudino-Sales &Peulvast, 2002; Fig. 2A).Therefore, the followingequation was used:

zðtÞ ¼ zðt � 1Þ þ RðtÞ � EðtÞ ð4Þ

under the condition that z ‡ 0, where z(t) is theheight of the water level above the surface at acertain month, R represents rainfall (millimetresper month) and E represents evaporation (milli-metres per month).To apply the model to climate variables within

NE Brazil, climatic time series were used basedon the following three input variables:

• Drift potential values representing the entirestudy area were taken from the closest grid pointof the NCEP/NCAR Reanalysis Project: 40�W;2Æ5�S (Fig. 3). This grid point was chosen as it islocated 65 km north-east of the Jericoacoara dunefield and based on its climatic properties (averageyearly wind speed above 5 m sec)1 at a height of10 m and relatively high correlations between thetime series of the wind speed and those of rainfallin Fortaleza). The modelled NCEP/NCAR winddata at this grid point (Fig. 3) were highly corre-lated with those measured in the airport ofFortaleza (R2 of 0Æ62, for monthly averages be-tween January 1974 and September 1996). Themodelled NCEP/NCAR values of wind speed



were higher than the measured values by 149% to190%, probably due to higher surface roughnessnear the Fortaleza airport, which is located withinthe city, about 13 km inland from the beach.• Rainfall time series were based on five grid

points (from the 50 year precipitation climatologyof Beck et al., 2005) located near the dune fieldsof Lencois Maranhenses and Jericoacoara (Fig. 3).• Potential evaporation rates were taken from

the nearest grid point of the NCEP/NCAR Reanal-ysis Project: 42Æ5�W; 2Æ5�S, located just 35 km fromthe Lencois Maranhenses dune field (Fig. 3).

The model was run each time for a differentcombination of the above three input variables,totalling 1 · 5 · 1 = 5 runs. Although the posi-tions of the grid points on which the model wasbased were not the same for the three variables(wind, rainfall and potential evaporation) becauseof differences in available grid resolution andspatial coverage (Fig. 3), considering the spatialextent of coastal dunes studied here, all the gridpoints used were sufficiently close (less than100 km) to the dune fields in the study areas.The model output (for each run) consisted of

the following six variables, calculated twice –firstly averaged for each month for the years 1948to 2005 and, secondly, summed over the monthsof each year:

• The number of months when an RDR wasformed (i.e. the number of months when rainfallexceeded potential evaporation).• The number of separate RDRs formed every

year (i.e. this may happen if interdune pondsformed and desiccated more than once during therainy season).• The height of the RDRs (this is also equiva-

lent to the level of water in the interdune ponds).• The width of the RDRs.• The expected dune movement rate as calcu-

lated from wind data.• The rate of dune movement based on the

distance between RDRs formed in consecutiveyears. The locations of the RDRs were taken fromthe average position between the location wherethe RDR started and ended in each year.

Model sensitivity and validation

The variability of the six output variables of themodel was analysed initially with respect to thevariability of the four input variables. Followingthat process, the correlation between the twooutput variables of dune movement rate (based on

wind power alone versus based on the distancebetween consecutive RDRs) was examined. Fi-nally, an external validation of the model wasconducted, by comparing the model results ofdune movement rates with actual dune displace-ment distances as measured on high spatialresolution satellite images (0Æ6 m). More specifi-cally, the yearly displacement of two barchandunes in the dune field of Jericoacoara (Fig. 3)was measured from QuickBird satellite images(spatial resolution of 0Æ6 m; acquired on 3 Sep-tember 2003 and 14 September 2004), using thesame method as in Levin & Ben-Dor (2004) andLevin (2006). In addition, several long series ofRDRs south-west of Manadacaru were digitizedfrom aerial photographs (at a scale of 1 : 15 000and spatial resolution of 2Æ5 m; acquired inNovember 1999 by the Brazilian Space AgencyINPE) (Figs 2E and 3). The linear correlationbetween the validation sets and the model runswere then calculated. In October 2006 (i.e. duringthe dry season, when most of the water betweenthe RDRs has already dried out), a field recon-naissance of selected RDRs was conducted in thecoastal dune fields of Pequenos Lencois andLencois Maranhenses, Maranhao, Brazil (Fig. 3).This study included the measurement of thespacing between RDRs along six transects andthe heights along three of these transects relativeto the local surface (in two of them the depres-sions between the RDRs were also measured).Vernacular names of plant species were obtainedby interviews with the local population and theLatin names were obtained in due course.

RESULTS

General characteristics of the climatic timeseries

Influenced by the location of the ITCZ, almost allthe climatic time series were correlated highlywith each other, especially at a monthly temporalresolution, and were somewhat weaker at a yearlytemporal resolution (Table 1). Rainfall in NEBrazil was negatively correlated with the poten-tial evaporation rate and with wind speed (orsand drift potential). In extreme El-Nino events(e.g. 1982/1983, 1997), rainfall was low andpotential evaporation rates and wind power werehigh (Fig. 4). When examined along the monthsof the year, most variables presented a clearseasonal pattern: March (and April) represented

10 N. Levin et al.


the centre of the rainy season, when rainfall wasat its yearly maximum and wind power at itsyearly minimum. September (and October) repre-sented the centre of the dry season, with anopposite pattern. High interannual variability wascommon to rainfall patterns, whereas potentialevaporation rates and wind power were lessvariable between years. On average, only in themonths of March, April and May was thereusually an excess of rainfall over the potentialevaporation rate, which may then lead to theformation of the RDRs that were the focus of thisstudy.

Model output and sensitivity analysis

Because the wind power in the study area is outof phase with the water level (corresponding tothe vegetation growth rate), vegetation growsfreely in the lee and lower part of the duneduring the wet season (February to May), whenthe wind velocity is below the threshold for sandmotion and then may be buried during thewindy season (September to December) whenmost of the dune motion occurs, leaving an RDRbehind. The main characteristics of the modeloutput can be appreciated from the time series ofthe 1950s (Fig. 5). The level of the water variedgreatly between different years; however, in mostyears there were at least two months when theinterdune ponds were flooded. Another phenom-enon should be noted; there were years whenrainfall was exceedingly low, so that interduneponds did not form at all (e.g. 1958, which isknown as one of the worst droughts of the 20thCentury; Fig. 5A and B; Hastenrath & Heller,1977; Rose, 1980). In these cases, the distancebetween two adjacent RDRs was large; however,this was not due to an excess in wind power in acertain year but rather because the spacing

between them represented two years or moreand not one.When examining all the model runs, it was

found that only in specific years did the modelpredict that no RDRs would form. One yearshould be noted especially here: the exceedinglydry year of 1958 (where all of the model runspredicted that no RDRs would form). Anotherissue that may hamper the detection of year toyear distance differences between RDRs is thetime of year when they were imaged. As theheight of the RDRs changes as a function ofthe monthly and yearly differences betweenrainfall and potential evaporation, some RDRsmay be under water during a certain month whileothers will remain above water (Fig. 2F). Thiseffect may lead again to an over-estimation of thedistance between adjacent RDRs when they aremapped from satellite images.The model simulations predicted the formation

of RDRs mainly between the months of February

Fig. 5. An example of the input and major output timeseries of the model for the following input variables: (i)wind speed data from NCEP/NCAR grid point at 40�W;2Æ5�S; and (ii) potential evaporation data from NCEP/NCAR grid point at 42Æ5�W; 2Æ5�S; rainfall data from42Æ25�W; 2Æ75�S. (A) Predicted water level (residualdune ridges height, in millimetres) with respect to time.(B) Predicted water level (residual dune ridges height,in millimetres) with respect to the position of thedunes (m).

Fig. 4. Climatic time series of the major variables,between the years 1948 to 2005.



and August, the peak months being March to Junewhen the probability for the formation of RDRswas above 80% (Fig. 6A). The largest increase inheight of the water level occurred in March andApril and the water level reached its peak heightin May (505 mm on average). The water level inthe interdune ponds decreased dramatically fromJune/July and was very low from August onwards(Fig. 6B). The formation of the RDRs themselvesis a function of the balance between rainfall and

potential evaporation and also of wind powerwhich controls the migration rate of the barchandunes. The number of years (within a modelsimulation) when no RDRs were predicted toform, decreased with annual rainfall (R2 = 0Æ22,P < 0Æ001, n = 58).Relative to the year 1975 (which was a year of

low wind intensity), yearly dune movement rates,as predicted by the model (based on wind poweralone), could be as much as 350% greater inwindy years (e.g. 1983). When calculating dunemovement based on the spacing between RDRs,the variability increased greatly reaching valuesthat may have been 700% greater in windy years.The increased variability in dune movement ratesbetween different scenarios of the model isprobably related to a ‘temporal shift’ in the dunemovement rates. In all years when RDRs werepredicted to form, the two model estimates ofyearly dune movement were almost the same(Pearson’s correlation value of 0Æ96 for the years1959 to 2004; lower plot in Fig. 7). When allyears, including the dry year of 1958 (when noRDRs were predicted to form) were taken intoaccount, the correlation value between the twomodel estimates of yearly dune movement waslower (r = 0Æ88; lower plot in Fig. 7). In theexample depicted in Fig. 7 (bottom plot), in1958, the model predicted that no RDR wouldform; therefore, the spacing between the RDRs forthe years 1957 and 1959 was quite large and willbe interpreted as the spacing between the RDRs of1958 and 1959. This discrepancy increased whenthe number of years with no RDRs as predicted bythe model increased. In scenarios where themodel predicted that in two years no RDRs wouldform (1958 and the El-Nino year of 1983), thecorrelation value dropped to 0Æ69. In scenarios inwhich the model predicted that in more thanthree years no RDRs would form, no correlation

A

B

Fig. 6. Monthly averages according to model simula-tions of the probability for the formation of residualdune ridges (A) and the water level in the inter duneponds (B). The error bars indicate one standard devia-tion above and below the average.

Fig. 7. The differences between themodelled yearly dune movementbased on wind data alone and basedon the spacing between residualdune ridges. These scenarios arebased on time series of two runs ofthe model, all for the same RDPseries, with different combinationsof rainfall and evaporation, leadingto scenarios where, in one or twoyears, the model predicted that noresidual dune ridges would form.

12 N. Levin et al.


was found between the two model estimates ofyearly dune movement.

Model validation

Validation from satellite imagesDune movement rates as extracted from satelliteimages (as in Figs 8 and 9) and aerial photo-graphs varied greatly between different dunes,not only in absolute values but more impor-tantly in the years when there was peak activityof dunes as well. The median dune movementrate in the different model scenarios rangedbetween 13Æ3 and 13Æ7 m year)1. The averagespacing between adjacent RDRs in the twovalidation sets of satellite images for Jericoaco-ara was 11Æ2 and 9Æ6 m. The spacings betweenadjacent RDRs for barchan no. 1 measured inthis study were highly correlated with modelpredictions: the best correlation for a singlescenario being r = 0Æ72 (P < 0Æ001, n = 35, 1969to 2003; Fig. 9), whereas in all other scenariosthe correlation was r = 0Æ56 (P < 0Æ001, n = 35).However, the spacing between adjacent RDRs forbarchan no. 2 was correlated poorly with model

predictions of annual dune movement rates, thebest correlation for a single scenario beingr = 0Æ30 (P = 0Æ06, n = 38), whereas in otherscenarios correlation values ranged between0Æ14 and 0Æ16.South-west of Mandacaru (in the deflation

plain upwind of the Lagoa Azul in the LencoisMaranhenses) there are several long series of

Fig. 8. Areas covered by sand as a consequence of movement of the dunes in the Jericoacoara coastal dune field,based on the residual dune ridges observed on QuickBird satellite images from September 2003 and September 2004.Dune no. 1 is shown (see text). Notice that some of the areas between the residual dune ridges are flooded and thatsome are not.

Fig. 9. Time series of dune displacement distances (m)as extracted from satellite images for barchan dune nos1 (shown in Fig. 8) and 2 in Jericoacoara. The results ofthe best model scenario are shown for comparison.



relatively old RDRs (on which a dense vegetationcover of trees and bushes has developed; Fig. 2E),reaching lengths of up to 7Æ5 km. Digitizing foursets of these RDRs (Fig. 10), the average spacingbetween the RDRs (in series where they wereeasily recognizable) ranged between 23Æ8 m (forthe western most series) to 36Æ5 m (for the easternmost series). These spacings were two to threetimes greater than those measured from thevalidation sets of Jericoacoara, indicating thateither dune movement rates were higher in thepast or that many of the RDRs had eroded andwere not visible any more.

Validation from field workSix transects were measured in the field to assessgeomorphological changes that the RDRs experi-ence with the passage of time (i.e. with distanceupwind from the stoss-side edge of a dune). Inthree of the transects, the vertical profile was alsomeasured (Fig. 11). The length of these transectsvaried between 257 and 615 m, the number ofRDRs detected along them varied between 18 and30 and the average spacing (displacements)between them varied between 15Æ1 and 29Æ3 m(Table 2). Generally, the surface upon which thedunes were advancing rose moderately at a slope

Fig. 10. Residual dune ridge series south-west of Mandacaru, Lencois Maranhenses, as digitized from aerial photo-graphs.

14 N. Levin et al.


ranging between 0Æ09% (in the Pequenos Lencoistransect) to 0Æ26% (in the Lagoa Azul transect),based on the negative correlation between theelevation of the edges of the RDRs and thedistance upwind from their respective dunes(Table 2; Fig. 11). In contrast to the satellite-derived displacements and with the temporalseries of wind data, it was found that in four ofthe six field transects there was a positive andsignificant correlation between the yearly dis-placements and the serial ID of the RDRs (corre-sponding to the number of years) upwind of thedune, as if the dune movement rates were higherin the past (Table 2; Fig. 12). The correlationbetween the yearly displacements as measured inthe field and model simulations was very poorand, in most cases, not significant. The averageheight of the RDRs as measured in the field was26Æ1 cm (standard deviation of 21Æ3 cm; n = 63),which was about half of the model-predictedmaximum water level (in May: 53Æ3 cm, with astandard deviation of 17Æ6 cm). The heights of theRDRs were not correlated with the distanceupwind of their respective dunes (i.e. the dunefrom which they were deposited). However, thewidths of the RDRs were correlated positivelywith distance upwind of their respective dunes(Table 2), indicating that the RDRs were wider asthe distance (upwind) from their respective duneincreased. As a result, the ratio between theheight and the width of the RDRs was correlatednegatively with the distance upwind of theirrespective dunes (Table 2), indicating that theRDRs attained a flatter shape (see Fig. 2C for an T

able

2.

Field

validationmeasu

rements

oftransects

across

RDRsupwindfrom

sixselecteddunes.

Number

inFig.3

Location

Variables

thatwere

measu

red

Length

of

transect(m

)

Numberof

RDRsalong

thetransect

Height

ofRDRs

(cm)

Average

displacement

(m)

Correlationbetw

een:

Displacement

anddistance

upwind

Width

ofRDRs

anddistance

upwind

Height/width

ofRDRsand

distanceupwind

1NearAtins

Profile

including

depressions

409

20

l=24Æ8

r=22Æ2

21Æ3

R=0Æ32n.s.,

n=19

R=0Æ27n.s.,

n=20

R=)0Æ48,

P=0Æ03,n=20

2In

thePequenos

Lencois

Profile

436

18

l=47Æ0

r=17Æ3

25Æ5

R=0Æ04n.s.,

n=17

R=0Æ55P=0Æ07,

n=12

R=)0Æ38n.s.,

n=12

34km

northofthe

LagoaAzul

Spacing

485

20

25Æ5

R=0Æ55P=0Æ01,

n=19

44km

northofthe

LagoaAzul

Spacing

497

18

29Æ3

R=0Æ46P=0Æ06,

n=17

5Nearthe

LagoaAzul

Profile

including

depressions

615

30

l=17Æ9

r=16Æ1

21Æ0

R=0Æ67P<0Æ001,

n=29

R=0Æ63P<0Æ001,

n=30

R=)0Æ37,

P=0Æ04,n=30

6NeartheLagoa

Azul

Spacing

257

18

15Æ1

R=0Æ47,P=0Æ05,

n=17

R=0Æ 67P=0Æ01,

n=13

Fig. 11. Field profiles across three sets of residualdune ridges, as measured in the field in the PequenosLencois, near Atins and near the Lagoa Azul (locationsin Fig. 1). The symbols on the profiles designate dif-ferent parts of the residual dune ridges: their highestpoint (centre), their edges (to the west and to the east)and the lowest point in between two residual duneridges (low). In cases where water was present, its levelwas also measured.



example of flattened RDRs that are now muchwider than the spacing between them). Themodel-predicted widths of the RDRs were corre-lated highly with annual rainfall (r = 0Æ77, n = 58,P < 0Æ001) and ranged between averages of 0Æ9and 5Æ5 m for the different scenarios. Thesevalues were similar to the measured values ofRDR widths in the field that ranged between 2Æ6and 5Æ5 m on average. Note that the width of themodel-predicted RDRs amounted on average to17% of the distance between adjacent RDRs.

DISCUSSION

Residual dune ridges, as found in the coastaldunes of NE Brazil (but also as far south as inCabo Frio near Rio de Janeiro: 42�02¢W; 22�54¢S),are found in other regions in the world. Theprerequisite conditions are alternating dry andrainy periods (which could be entirely non-seasonal) so that, at times, there is enough rainto flood deflation plains basins or interduneslacks. Examples of such areas can be found inthe north of Queensland (Australia; 145�10¢E;14�58¢S; Pye, 1982) as well as in California (Baye& Wright, 2004). It is the extensive area coveredby these RDRs in NE Brazil that makes this areaunique; this is because of the combination ofactive dunes in a humid climate. Where longseries of RDRs exist (e.g. south-west of Manda-caru, Lencois), it is quite probable that not all ofthe RDRs which originally formed still exist(because of erosion by wind, water and thegrowth of trees and bushes). Thus, if X RDRs areobserved over a certain distance upwind from abarchan dune, there may have originally beenX + Y RDRs, where the number of RDRs that haveeroded (Y) is not known. Therefore, the observed

average spacing between the X RDRs should beinterpreted as the maximum possible values ofyearly dune movement (presuming that some ofthe RDRs have disappeared). Based on the aver-age spacing of 23Æ8 m (as digitized from the longseries of RDRs south-west of Mandacaru) and thedistance of about 14Æ5 km (which is separating thedunes near the Lagoa Azul from the PreguicasRiver; see Fig. 3), it took these dunes at least609 years to reach their current position. How-ever, this time span should be regarded as aminimum time frame, as it is very probable thatmany RDRs that formed in the past were erodedand are not visible today.Dune displacements between consecutive RDRs

were measured using both field work and satelliteimages/aerial photographs. Each of these methodshas certain advantages. Using field work, it waspossible to measure the elevation profiles alongtransects and to study what plant species exist onthe RDRs and in the low depressions betweenthem. However, in most cases these RDRs do notfully retain their arcuate shape as time goes by. Asa result, by using high spatial resolution satelliteimages (or aerial photographs) it is easier to detectthem, even when they are not continuous (unlessthese images were acquired when many of thespaces between the RDRs were covered by water,hiding some of the RDRs under the water level). Itseems that identifying the position of the RDRsfrom satellite images was more reliable than inthe field, because: (i) there are no sharp lines inreality defining the exact location where a RDRbegins; rather, like other natural phenomena,their boundaries should be defined by the rateof change in ground elevation, slope and vegeta-tion cover; and (ii) in the field transects, each RDRwas sampled at just one point. As the width of theRDRs is not constant and as they are not pre-served in full as the years go by it is more accurateto define their location using remote-sensingplatforms. The model predicted the heights andwidths of the RDRs quite well. The model-predicted heights were only 27 cm higher thanaverage measured heights in the field. Possibleexplanations for this height difference betweenthe modelled and measured RDRs may be relatedeither to the simulated climate data that are inputinto the model and/or basic assumptions of therelationship between precipitation and evapo-transpiration.The overall correlations between model-

predicted time series of dune movement ratesand the measured displacements of dunes asmeasured from satellite images or in the field

Fig. 12. Spacing between sequential residual duneridges as measured in the field in the Lagoa Azul profile(no. 5 in Table 2).

16 N. Levin et al.


were quite low (except for dune no. 1 in Jerico-acoara: r = 0Æ72). However, it seems that themodel has succeeded in capturing and quantify-ing the basic components of the system that werepreviously described in a qualitative manner byJimenez et al. (1999) and by Claudino-Sales &Peulvast (2002). These components include thehigher movement rate of the dunes during the dryseason, the formation of the RDRs during the wetseason, as a consequence of excess rainfall overevaporation, and the temporal variability in theirformation both within years and between years.As regards the temporal variability in the forma-tion of the RDRs within years, the model hasdemonstrated that, depending on the balancebetween rainfall and evaporation, RDRs may formduring every month but mostly between Januaryand August (Fig. 6A). Therefore, the displace-ment between adjacent RDRs does not representthe distance moved by a dune during 12 months.Rather, it is the distance moved by a dune duringthe dry season, a time period that may be smalleror greater than 12 months. Generally, the assump-tion that these displacements correspond to theyearly movement of the dunes is true in this area.However, occasionally there may be years whenno RDRs form; this will happen in years whenrainfall amounts in NE Brazil are well belownormal (as might happen in extreme El-Ninoevents). In these cases the displacement betweentwo RDRs represents two years or more and notone, leading to lower correlation between cli-matic time series of wind power (or correspond-ing variables) and dune displacement distances(Fig. 7). Investigators should therefore be awarethat a gap between two RDRs may sometimesrepresent more than one year. Even when RDRsare formed every year (during the wet season), itis rare for them to be preserved in full for manyyears. When RDRs are formed between dunes,then the dunes upwind will cover the RDRscreated by the dune downwind, depending on thedistance between them (as in Jericoacoara; Fig. 8).However, the integrity of RDRs is not onlythreatened by migrating dunes. The completenessand continuity of the arcuate RDRs in the defla-tion areas upwind of the dune areas in theLencois Maranhenses or in the Pequenos Lencoisis also a function of the combination of hydro-logical, aeolian and biotic factors.In the preliminary stages, the plants established

on the RDRs are perennial herbaceous types, suchas the Capim (a name referring in this area tovarious plants from the families of Cyperaceaeand Poaceae; nomenclature based on Matias &

Nunes, 2001; and other sources), Salsa (Ipomoeaspp.) and the Cipo-da-praia (Remirea maritima).Later on, various bushes and trees may developon the RDRs, such as the Cajueiro (Anacardiumoccidentale), Cajuı (Pouteria caimito), Cajueiro doMato (Curatella americana), Guajiru (Chrysobal-anus icaco), Murici (Byrsonima spp.), Jatoba(Hymenaea spp.), Mirim (Humiria balsamifera)and Puca (Mouriri pusa) (Fig. 2D). These plantswere found to develop in most cases on RDRswhose order was about a 10th or more upwind ofthe dune that formed them. There were placeswhere vegetation on the RDRs did not includelarge bushes or trees, for example, in field transectno. 2 (in the Pequenos Lencois) or in many of theRDRs in Jericoacoara. A possible explanation forthese cases is that these are flat areas where windflow is unobstructed from the coastline inwardsby mangrove (or other tall) vegetation, so that thewind speed and sand movement do not allowtrees and shrubs to become established. Even inthe more mature stages, on RDRs that date severalhundred years ago (as those near Mandacaru, inthe Lencois Maranhenses), trees do not establishin the low-lying areas between the RDRs (proba-bly due to seasonal flooding) and these areas aredominated by small bushes such as the Vassour-inha (plants from the Rubiaceae family; Fig. 2E).The establishment of plants on the RDRs mod-

ifies the wind flow and leads to modifications inthe shape of the RDRs as various nebkhas form onthem. These nebkhas may lead to wind erodingsand from RDRs in certain parts, whereas in otherparts sand will be deposited and the height andwidth of the RDR will increase. The discrepancybetween the modelled and measured widths ofthe RDRs may be because the width of RDRsincreases with time due to trapping of sand byplants of the RDRs and due to their flattening bywater erosion. In addition to these aeolian pro-cesses, the RDRs are under the influence ofhydrological processes. Ephemeral rivulets mayform in the deflation areas, breaching the RDRs.Additionally, the flow of water over and betweenthe RDRs may lead to the erosion and resedimen-tation of the sand grains forming these RDRs. Theconsequences of all these processes combinedwith trampling by animals (e.g. cattle) and humandisruptions are the reason for the RDRs to losetheir initial coherent arcuate form with time andeventually to disappear. In fact, the long series ofdozens or even hundreds of RDRs to the southand south-west of Mandacaru (Figs 3 and 10) arequite an exception, even for NE Brazil whereRDRs are quite abundant.



In the field measurements a positive andsignificant correlation was found between theyearly displacements and the ID of the RDRscounted upwind from the dune (corresponding tothe number of years), as if the dune movementrates were higher in the past. Had there indeedbeen a change in dune size with time because ofincreasing mergers between dunes, this wouldhave been evident from the shape and size of theRDRs as seen on the aerial photographs. However,no evidence was found that this is the case(Fig. 10). Rather, it is contended that the erosionand consequent disappearance of some parts ofthe RDRs with time leads to greater spacingbetween them upwind of a dune when measuredalong a transect in the field.

CONCLUSIONS

It has been shown that the formation and spacingof residual dune ridges that form behind migrat-ing dunes due to the rise and fall and water levelscan be modelled well using climatic time series ofrainfall, potential evaporation and wind power.The model succeeded in predicting the width andheight of RDRs as well as the spacing betweenthem. However, because of the growth of plantsand subsequent aeolian and hydrological pro-cesses, these arcuate vegetated RDRs do notpreserve their initial shape for long periods. Astime passes, they are usually flattened and maydisappear entirely. In conclusion, the potential ofsuch RDRs for serving as the equivalent of treerings to reconstruct the palaeo-climate of windregime on a yearly basis or to identify pastEl-Nino events seems to be quite limited becauseof two major reasons: (i) occasionally there areyears with low rainfall when no RDR forms; and(ii) the RDRs do not retain their original shapeand change in shape and size with time becauseof natural erosion processes and the ecologicalsuccession of plants on them.

ACKNOWLEDGEMENTS

Wewould like to thank Baruch Ziv from the OpenUniversity of Israel for his help with NCEP/NCARdata and Efrat Morin from the Hebrew Universityof Jerusalem for fruitful discussions on modelbuilding using Matlab. Julio Andrade and JulianaChristina Fukuda from IBAMA (Lencois Maran-henses National Park) helped us in organizing thefield trips, whereas Afonso Celso Castro Carvalho,

Teogenes do Carmo Reis, Cural Bernardo and JoseRoberto Garcia Oliveira (all from Barreirinhas,Maranhao, Brazil) helped us in measuring theprofiles of RDRs in the field. Fortaleza rainfalldata was made available from The NationalCenter for Atmospheric Research and the non-profit University Corporation for AtmosphericResearch (UCAR). Rainfall data for other stationsin Ceara was obtained from the Fundacao Cea-rense de Meteorologia e Recursos Hıdricos, FUN-CEME: The Ceara Foundation for Metrology andHydrologic Resources. Juliane Sander helped intranslating the Paul (1944) paper from Germaninto English. We appreciate the remarks made byAndreas Baas and by the anonymous refereesand thank them for their contribution to theimprovement of this manuscript. This study hasbeen funded by the Volkswagen Foundation(Volkswagen-Stiftung) (http://www.volkswagen-stiftung.de/), as part of the following research:‘The palaeoclimate and environmental implica-tions of the aeolian sand encroachments into thecoast of Ceara State, NE Brazil’. The KreitmanFellowship Foundation has supported NoamLevin in his post-doctoral research.

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Manuscript received 27 February 2008; revisionaccepted 11 December 2008



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