a recharge model for high altitude, arid, andean aquifers

HYDROLOGICAL PROCESSESHydrol. Process. 23, 2383–2393 (2009)Published online 13 May 2009 in Wiley InterScience(www.interscience.wiley.com) DOI: 10.1002/hyp.7350

A recharge model for high altitude, arid, Andean aquifers

John Houston*20 Six Acres, Shrewsbury, SY3 6AF, UK

Abstract:

Evidence for groundwater recharge in arid zones is mounting, despite early ideas that recharge was unlikely where evaporationgreatly exceeded precipitation. The mechanisms and magnitude of groundwater recharge in the Andes and Atacama Desertare not well known but the subject of current research. Diffuse recharge is expected to be limited to high altitude areas withcoarse-grained soils devoid of vegetation. A recharge model for this environment is developed based on a simple soil moisturebudgeting technique and the calculation of actual evaporation based on empirical studies. The model is run with data for theLinzor basins, over 4000 m elevation at 22Ð2 °S on the west slope of the Andes. It is checked against independent estimatesbased on the chloride mass balance (CMB) method and flood events measured downstream in the Rıo Salado and found toprovide robust and reliable results. The results indicate that irregular and volumetrically limited amounts of diffuse rechargeoccur at high elevations in half of all years, with a tendency to cluster during La Nina episodes. For the Linzor Basins, meanannual recharge is found to be equivalent to 28 mm a�1, although no recharge occurs in years with precipitation less than120 mm, and increases proportionately with annual rainfall amounts above this limit. Copyright 2009 John Wiley & Sons,Ltd.Additional Supporting information may be found in the online version of this article.

KEY WORDS groundwater recharge; actual evaporation; soil moisture budget; recharge model; La Nina; Atacama Desert; centralAndes

Received 3 December 2008; Accepted 5 April 2009

INTRODUCTION

Groundwater recharge processes in arid zones have beenwidely documented (Gee and Hillel, 1988; Lerner et al.,1990; Stephens, 1993; Allison et al., 1994; Simmers,1997; Hogan et al., 2004; Scanlon et al., 2006). Directrecharge from precipitation is perhaps the most chal-lenging process to quantify because of scant and highlyvariable precipitation. Coupled with the uptake of infil-tration by native vegetation in the root zone, the resultis low flux rates to the water table. Chemical and iso-topic tracer methods are generally thought to provide themost reliable quantification techniques (Dettinger, 1989;Allison et al., 1994; Houston, 2007). Physical methods,such as lysimetry or soil water flux calculations usingDarcy’s or Richard’s equations require data that are dif-ficult to obtain and represent point measurements (Geeand Hillel, 1988; Allison et al., 1994). Soil moisture bal-ance methods have generally been considered subject tolarge errors (Gee and Hillel, 1988; Allison et al., 1994).Nevertheless, they remain popular because they can beapplied at basin scales over long time spans with com-monly measured meteorological data and easily obtainedinfiltration data (Lerner et al., 1990; Rushton, 2003). Theprincipal requirement for reliable estimation of rechargeusing the soil moisture balance method is the accuraterepresentation of the evaporation process.

* Correspondence to: John Houston, 20 Six Acres, Shrewsbury, SY3 6AF,UK. E-mail: [email protected]

This article introduces and evaluates a conceptual andquantitative model for diffuse recharge to high altitude,arid aquifers in the central Andes based on a soil moisturebudgeting approach. An evaporation function for bare soilabove the vegetation limit is specifically developed forthis environment. Figure 1 is a location map of the areashowing places mentioned in the text.

The occurrence of groundwater in the Andes presentsunique features not widely encountered in hydrogeolog-ical studies. Aquifers are frequently compartmentalizedas a result of tectonic activity and uplift of volcano-sedimentary basins, and occur over an extreme ele-vational range. Evidence for widespread present dayrecharge to groundwater in the central, high Andes is con-tinuing to mount (Magaritz et al., 1990; Aravena, 1995;Grilli et al., 1999; Herrera et al., 2006; Houston, 2007)despite some suggestions to the contrary (Grosjean et al.,1995). The perennial nature of the major rivers drainingthe western slope of the Andes, regardless of the bulk ofprecipitation being limited to a few months in the aus-tral summer, is proof enough that they are maintainedby groundwater discharge. This requires regular rechargeunder current climatic conditions, yet the mechanismsand magnitude of such recharge remain poorly knownand imprecisely quantified.

The importance of quantifying recharge as a prereq-uisite for water resource studies and development isobvious. Currently, a model that equates recharge tomean annual precipitation less the mean annual evap-oration at successive elevations is in routine use forresource evaluation in the region. This model does not

Copyright 2009 John Wiley & Sons, Ltd.

2384 J. HOUSTON

Figure 1. Digital elevation model of the central Andes (GOTOPO30) showing the location of the Rıo Loa Basin and Linzor near the crest of thedrainage divide

take into account the considerable variations in annual,seasonal and daily precipitation (Houston, 2006a), northe limitation of evaporation as a result of lack of avail-able moisture (Houston, 2006b), and as a consequenceis unrealistic and unlikely to provide reliable estimatesof recharge. Also in widespread use is the techniquebased on an evaluation of the water balance for indi-vidual catchments, but the errors associated with thismethod cannot be clearly defined. The individual fluxerrors are frequently not estimated independently, andmay accumulate in the recharge term. Furthermore, anyinter-basin groundwater flow would render this approachinvalid (Montgomery et al., 2003). Many studies haveconcentrated on the analysis of stable isotopes to assessrecharge and groundwater flow regimes (Magaritz et al.,1989; Aravena, 1995), but groundwater samples for thesestudies are frequently taken from pumped wells open tostratified or multiple aquifers, rendering their interpreta-tions subject to ambiguities. Based on the chloride massbalance (CMB) method, Houston (2007) suggested thatrecharge in the Western Cordillera increases exponen-tially with elevation in parallel with precipitation.

Recent studies in the Mojave and Chihuahuan desertsof the United States show that even in arid environments,there is frequently sufficient vegetation to capture mostif not all moisture that infiltrates to the root zone, pre-cluding deeper percolation to the water table (Walvoordand Scanlon, 2004). Consequently, these authors arguethat most groundwater recharge is highly dependent onlocalized or point sources under ephemeral channels orthrough fissures and faults, although diffuse recharge mayoccur in non-vegetated areas, as confirmed in the reviewby Stephens (1993).

A global study of 26 large, natural desert basins forwhich reliable estimates of bulk recharge are availablesuggests that the mean rainfall threshold for rechargeto occur is approximately 100 mm a�1, although thereis a considerable range between 10 and 200 mm a�1

(Scanlon et al., 2006). In the central Western Cordilleraof the Andes, spatial variations in precipitation occur withboth latitude and elevation (Houston and Hartley, 2003).Between 24 and 28 °S mean annual rainfall generallyexceeds 100 mm a�1 at 4000 m. North and south of theselimits mean annual rainfall increases to 500 mm a�1 at

4000 m by 18 °S and 32 °S respectively. Precipitationrapidly increases with elevation, reaching an estimated150 mm a�1 at 4600 m even within the driest latitudes.

Over 80% of intra-annual precipitation occurs asrainfall during the austral summer (Houston, 2006a), theremainder tending to fall as snow during the winter,with a significant proportion sublimating directly intothe atmosphere (Vuille and Ammann, 1997). Inter-annualprecipitation varies over at least a threefold range dueto the climatic impact of El Nino-Southern Oscillation(ENSO). High (low) rainfall is usually associated with LaNina (El Nino) in the Altiplano and Western Cordillera(Vuille, 1999; Garreaud and Aceituno, 2001). Studies byScanlon et al. (2005) have shown that higher than normalrainfall due to ENSO variability leads to increased growthof vegetation and reduced percolation in the MojaveDesert. But at high altitude in the Andes, increasedrainfall as a result of ENSO variations is unlikely toresult in rapid vegetation expansion since increasedprecipitation correlates with decreased temperature andincreased exposure (wind strength) on both daily andmonthly timescales (Houston, 2006b).

Pan evaporation (after correction, equivalent to poten-tial evaporation) is negatively correlated with elevationand temperature, reducing by ca. 600 mm a�1 for every1000 m gain in altitude (Houston, 2006b). Actual evap-oration however, is limited by available moisture anddiminishes rapidly as the level of soil moisture saturationdrops below the surface.

Diffuse (direct) groundwater recharge might thereforebe expected to occur where vegetation is sparse or non-existent, where coarse-grained immature volcanic soilsallow high infiltration rates, at high altitudes whereprecipitation is at a maximum and evaporation is at aminimum, and particularly in those seasons where ENSOand related meteorological factors lead to increased dailyand annual precipitation intensity over sustained timeperiods allowing soil moisture deficits to be reduced.

THE CONCEPTUAL MODEL

The recharge model developed here is based on thewidely used principle of soil moisture budget accounting(Gee and Hillel, 1988; Lerner et al., 1990; Simmers,

Copyright 2009 John Wiley & Sons, Ltd. Hydrol. Process. 23, 2383–2393 (2009)DOI: 10.1002/hyp

A RECHARGE MODEL FOR HIGH ALTITUDE, ARID, ANDEAN AQUIFERS 2385

Figure 2. Conceptual model showing fluxes, storage, and choke pointsfor recharge to high altitude, arid, Andean aquifers

1997; Rushton, 2003) where the elements and fluxes areshown in Figure 2 and given by the following equation:

RE D RF � RO � Eactual � Sm

where RE is groundwater recharge, RF is precipitation,RO is surface water runoff, Eactual is the actual evapora-tion and Sm is the change in soil moisture storage.

The key to this approach lies in estimating the actualevaporation allowed by the availability of soil moisture.It has the advantage of using independent data that isgathered routinely (rainfall, pan evaporation), or can beobtained from simple field tests (soil characteristics),and can therefore be used on a routine basis. Thistype of model was originally designed to incorporatethe effects of transpiration from vegetation having beendeveloped for humid climates (Calder et al., 1983),although it has been applied with some success to semi-arid climates (e.g. Houston, 1990; Rushton, 2003). Themodel conceptualization implemented here specificallyexcludes the impact of transpiration and applies only tobare soils for reasons discussed below. Errors associatedwith this method may be large unless the input parameters(rainfall, evaporation and soil properties) are accuratelyknown, and are based on daily data (Howard and Lloyd,1979). Ideally there should be one or more meansfor checking the output, such as calibrating modelledrecharge against water level fluctuations or modelledrunoff against observed runoff, or by comparison withalternative methods for estimating recharge (Lerner et al.,1990).

In operation, the model assumes that at the soilsurface, precipitation infiltrates up to a critical limit: theinfiltration capacity of the soil. Precipitation in excess ofthe infiltration capacity is routed as direct runoff (Hortonoverland flow). Water entering the soil replenishes anypreviously existing deficit up to the field capacity. Soilwater evaporation is limited by the actual moisturecontent such that when there is no deficit, evaporationtakes place at a maximum (potential) rate, decreasingthereafter as a soil moisture deficit builds up until acritical point is reached when evaporation effectively

ceases. The deficit is assumed to build downwards fromthe ground (evaporating) surface, reaching a maximumat the extinction depth. This leads to the concept of adepth to saturation, equivalent to the soil moisture deficitdivided by the field capacity (less unavailable water heldat very high suction potentials). This is a convenientcomputational equivalence and does not imply that undernatural conditions the soil moisture content suddenlychanges from a maximum to that at field capacity. Themodel assumes that for bare soils, any infiltrated waterin excess of the soil moisture (field) capacity is free todrain below the extinction depth.

Once the potential recharge has moved below theextinction depth for evaporation, deep percolation isassumed to occur through the soil or rock of the vadosezone by piston flow. Assuming no change over timein the moisture content of the vadose zone belowthe extinction depth, potential recharge is equivalentto actual recharge. Modifications to this approach maybe made where adequate data exist on the hydraulicproperties and conditions in the vadose zone below theextinction depth, or may be simulated using a transferfunction approach. This may be particularly relevantif it is suspected that preferential pathways such asfissure systems exist allowing infiltration to bypass thesoil zone, or alternatively if low permeability horizonssuch as welded ignimbrites exist that would retarddeep percolation. In practice, the requirement for suchmodifications to simulate specific catchments effectivelywithin the model will quickly become apparent duringcalibration.

The data required to run this model therefore includea sufficiently long time series of daily rainfall andevaporation (at least ten years of daily data to allow forENSO related fluctuations). This data has been widelygathered throughout the Andes on a routine basis overmany years, and is readily available (Houston and Hartley2003; Houston 2006a,b). In addition, knowledge of theinfiltration characteristics of the soils, the soil moisturecapacity and the response of evaporation to varying soilmoisture conditions is required. Although not widelyavailable, such data may be easily obtained from fieldtests and literature estimates as described below.

Once specified, the conceptual model should be cal-ibrated and validated against independent estimates ofrecharge such as tracer techniques, recession curve anal-ysis, or stream and groundwater hydrographs.

IMPACT OF DESERT VEGETATION ON DIFFUSERECHARGE

Recent studies (Gee et al., 1994; Walvoord and Scanlon,2004) have shown that the indiscriminate use of soilmoisture budgeting methods in arid environments islikely to be unwise since most, if not all, soil moisturereplenishment is used by plants leading to maximumsuction potentials in the root zone, creating a divergentflux plane such that soil moisture below this depth


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Figure 3. Phytogeography related to elevation in the upper Rıo Loa Basin. Vegetation types and cover (left) modified from Villagran et al. (1980).Plant frequency and root cover (right) from this study

is drawn upwards precluding recharge to groundwater.Hence, a recharge model for the arid Andes must considerthe vegetation cover.

Vegetation in the Western Cordillera ranges fromapproximately 2700 to 4400 m as shown in Figure 3(Villagran et al., 1981). The lower limit of vegetationis controlled by the paucity of moisture, whilst theupper limit of vegetation is controlled by temperatureand exposure (Gutierrez et al., 1998), and above 4100 mthe soil zone is largely bare. In the Rıo Loa Basin(22 °S) vegetation reaches a maximum cover of 20–30%between 3200 and 4100 m, dropping rapidly above thisto its limit at 4400 m. With this relatively low plantcover it might be assumed that an opportunity exists fordirect recharge to occur in proportion to the coverage. Yettransect excavations of the soil zone to depths up to 1 mmade for this study to test the extent of the rooting systemshow that this is unlikely (see Supporting Information).The Puna zone (3200–3800 m) is dominated by woodyshrubs, where plant frequency is typically around 20 per100 m2, whereas the High Andean zone (3800–4100 m)is dominated by grasses, and plant frequency is almostdouble. A shallow root mat for both woody shrubsand grasses radiates out from the axis of each plantat soil depths of 10–30 cm. Each plant extends itsroot mat to compete with its neighbour, resulting in100% coverage between 3500–4000 m in the Puna andHigh Andean zones. This suggests that the root systemsextract all available soil moisture, and plant densityis determined by the physiological requirements of thedifferent species and the ability of their root systemsto extract adequate moisture. Hence, a diffuse rechargemodel for the arid Andes is best restricted to high altitudeareas above 4000 m where there is little or no vegetationto extract soil moisture, except where there is independentconfirmation for diffuse recharge below this elevation.

INFILTRATION CHARACTERISTICS AND SOILMOISTURE CAPACITY

Soils in the high altitude, arid Andes are generally coarse-grained, immature, Andisols, due to a combination of

lack of weathering consequent on hyper-aridity, recent(Pleistocene-Holocene) effusive volcanic activity, and toa limited extent, Pleistocene glacial activity.

These Andisols present only shallow (<0Ð5 m) alter-ation from their parent rocks with an ablative skin ofresidual coarse gravel overlying a generally finer grainedB horizon (see Supporting Information). In some basinsplaya deposits have formed as a result of largely end-horeic drainage. The soils overlying playa deposits arelargely immature Entisols rich in evaporitic mineralsand sometimes saturated near playa centres but rapidlycoarsen to sandflat alluvium around the central playa. Thevariation in soil characteristics reflects the distribution ofthe underlying parent material or geology.

A study of the infiltration characteristics of these soilsusing double ring infiltrometers installed to a depth ofca. 0Ð5 m gives results ranging over three orders of mag-nitude (Table I). Infiltration rates are significantly cor-related with the grain size of the soils and drainagedensity indicating that it is possible to extrapolate pointsource measurements up to catchment scale (see Sup-porting Information). Pleistocene tephra and lava havehigh infiltration rates (5–50 mm d�1) and form the basisfor the majority of soils in the high Andes. Some alluvialsoils and glacial moraine have very high infiltration rates,whereas Mio-Pliocene volcanic soils and those of salineplayas tend to have considerably reduced infiltration ratesand this is reflected in their very low permeability. Athigh elevations, precipitation intensity exceeds 5 mm d�1

on an average of 10 days per year, whilst 50 mm d�1

has a return period of ca. 12 years. Hence, runoff willoccur rapidly every year from Quaternary lava and Mio-Pliocene volcanics, but Quaternary tephra and glacialmoraine will tend to allow most precipitation to infiltrate,and this is confirmed by direct observation.

Maximum soil moisture capacity is the product ofthe soil thickness and its field capacity (less unavail-able water). In this context, the thickness of the soil zonewhether soil or parent material, is taken to be 2 m, equiv-alent to the extinction depth for evaporation as describedbelow. Field capacity may be estimated in a number ofways based on field measurement, empirical or theoretical



Table I. Infiltration rates, grain size and drainage density for different soil types in, or near the Linzor catchments. The infiltrationrate is for a period of 24 hours and is determined by extrapolating the infiltrometer data (see Supporting Information) using a best

fit power function and integrating the area under the curve

Location Soil type Infiltration rate (mm d�1) Grain size d50 mm Drainage density km km�2

Pampa Pieneta Sandflat alluvium 140 0Ð70 0Ð30Linzor Glacial moraine 121 0Ð80 0Ð20Linzor Pleistocene tephra 27 0Ð40 0Ð15Toconce Toconce Fm sediments 18 0Ð45 0Ð58Linzor Pleistocene lava 5 0Ð35 1Ð30Toconce Puripicar ignimbrite 1Ð2 0Ð25 1Ð48Turi Saline alluvium 0Ð22 0Ð37 —Toconce Sifon ignimbrite 0Ð21 0Ð30 2Ð35

relationships (e.g. Hillel, 1982; Stephens, 1995). In orderto develop a model that is readily usable in situationswith limited data availability, this implementation uses arange of literature values relating field capacity to soilgranulometry (see Supporting Information). Such val-ues may be refined using a power curve representationfor the soil moisture characteristic developed by Clappand Hornberger (1978). Unavailable water held at suc-tion potentials greater than ca. �1500 kPa is assumedto be negligible, although if this assumption is incorrect,recharge will be greater than calculated. Hence the modelis conservative in this respect.

CALCULATION OF ACTUAL EVAPORATION

A study of evaporation throughout the Atacama Desert(Houston, 2006b) allows the development of a conceptualframework for actual soil moisture evaporation to beestablished. Above the inversion layer at ca. 1000 m,75% of the variance in Class A pan evaporation iscontrolled by temperature, resulting in a linear decreasewith the lapse rate and enabling the estimation of panevaporation at locations and over areas where no dataexists:

Epan D 4364 � �0Ð59A�

where Epan is in mm a�1, and A is the altitude in m. Epan

can be corrected to open water or maximum potentialevaporation from a bare soil surface (Epot) using a panfactor of 0Ð9 for fresh water.

Evaporation from a wide variety of arid zone bare soilsurfaces with differing grain size distributions tends tobehave in a similar way as a result of the very high suc-tion potentials (<�10, 000 kPa) that can develop at thesurface in such environments (Scanlon, 1994; Coudrain-Ribstein et al., 1998). Empirical studies demonstrate thatevaporation declines exponentially with depth to thewater table, effectively extinguishing at a depth of 2 m(Figure 4). In general terms, actual evaporation is reliablysimulated by an equation of the form:

Eactual D G e��kd�

where G is the intercept at the ground surface, effectivelyequivalent to potential evaporation, k is a constant and d

Figure 4. Relationship between actual evaporation and depth to watertable in the Andes and Atacama Desert. Redrawn from sources indicated

is the depth to the water table, taken to be equivalent todepth to saturation as previously defined.

For mean daily evaporation at the Salar de Atacama(2300 m) G D 7Ð04 mm and k D 0Ð0027 when d is inmm. Where daily data are available, G may be replacedby the corrected pan data. Where no data are available,mean annual G may be estimated from the equation forEpan versus elevation, and then corrected by the panfactor and converted to a daily value. Fluctuations inevaporation through the year may be approximated byfactoring with the monthly fractional values given inHouston (2006b). Studies by Grilli et al. (1986, 1989)and Houston (2006b) point to the probability that k mayalso vary with elevation according to:

k D �1Ð3 ð 10�3 � 6Ð0 ð 10�7A

although, since this is based on only two studies, careneeds to be taken to evaluate the impact of varying kuntil further data become available.

UNSATURATED ZONE TRANSFERAND RECHARGE

Once infiltration passes the soil zone to become percola-tion in the vadose zone, the transfer of water is subjectto a variety of processes, including gravity, capillary andadsorptive forces, hysteresis and redistribution as wellas being subject to moisture and matrix heterogeneities


2388 J. HOUSTON

(Hillel, 1982; Stephens, 1995). However, below coarse-grained, bare soils gravity drainage dominates and themoisture content is unlikely to fall below field capac-ity. This has been confirmed by direct observation andmeasurement (Gee et al., 1994). Gravity drainage of per-colation may take place by piston flow or may be subjectto redistribution over time.

This model assumes piston flow with any moistureentering the top of the profile being compensated by anequal amount exiting the base of the zone (the watertable) to become recharge. Piston flow is computation-ally convenient, although an increase in soil moisture atthe top of the vadose zone may lead to the developmentof a downward hydraulic gradient and redistribution overtime. The time lag involved in redistribution depends onthe thickness of the unsaturated zone, the unsaturated ver-tical hydraulic conductivity and the degree of saturation.Such data is normally not available in this environment,and therefore daily recharge calculated by the model maybe over or underestimated if redistribution is a signifi-cant factor. Nevertheless, for most studies daily valuesof recharge are not needed, and if the cumulative wetseason moisture input is assumed to redistribute throughthe profile during the ensuing dry season, then S willremain approximately constant on an annual basis. In thisway, annual values of recharge calculated by the modelwill provide the dependable information.

MODEL OPERATION

Based on these relationships the recharge model maybe built using what might be termed classical soilmoisture budgeting methods. Daily precipitation data arerequired as input, and any amount in excess of theinfiltration capacity is considered as direct runoff (Hortonoverland flow), the balance constituting infiltration. Thesoil moisture content at the start of a period (day) isequal to the antecedent soil moisture plus the infiltration,limited by the maximum soil moisture capacity. Thisvalue is calculated as the product of the soil thicknessand estimated field capacity. If the daily soil moisturecontent exceeds the maximum capacity, the excess isassumed to percolate to deeper zones, beyond the reachof evaporative forces, and becomes potential recharge.Assuming no change in moisture storage below theextinction level and piston flow, potential recharge isequivalent to actual recharge.

The soil moisture content at the end of the periodis then calculated by subtracting the actual evaporationfrom the sum of the start soil moisture, infiltration andpercolation (taken as negative). Actual evaporation iscalculated as described above, preferably starting withmeasured daily pan evaporation data, corrected, and inputas a daily G value, but using estimated values where theseare not available. Depth to saturation (d) is calculated asthe soil moisture deficit divided by the field capacity.

Variations to this procedure may be added to improveresults and/or reflect whole basins. Such variations might

include for example, a lag term to represent the passageof the potential recharge through a thick vadose zone, oran interflow factor to divert some of the percolation tosurface water runoff, either with or without a lag term.For the calculation of recharge to a whole basin, pointvalues may be factored by their area within the catchmentto arrive at areal values. Since Andean basins extendover significant altitudinal ranges it is suggested thatany model be subdivided into several elevational zoneswith the parameters varied accordingly. If precipitationmeasurements are not available from multiple sites ina catchment, they may be estimated by factoring oneor more nearby station data according to the elevationdifference based on the following formula (Houston andHartley, 2003):

RF D e�0Ð0012A

where RF is in mm, and A in m above sea level.The rationale for varying evaporation with elevation hasalready been described. For areal estimates of infiltrationcapacity, mapping the extent of the different soil typeswithin the basin, and then weighting the value for eachby its area can made.

The model requires an initial start soil moisture capac-ity to be estimated. Trying a range of values will soonindicate a suitable choice, or alternatively a stabilizingperiod may be introduced using average values. As anexample of the functioning of the recharge model, theresponse to an input rainfall may be tested (Figure 5).On the first rain-day, infiltration allows the soil moisturedeficit to begin reducing, such that by day six of the rain-fall event, soil moisture capacity reaches its maximum. Inparallel with the decreasing soil moisture deficit, actualevaporation increases until it too reaches a maximum(potential evaporation) by day six. Once the maximumsoil moisture capacity has been reached, further infiltra-tion results in the transfer of water across the extinctioninterface, and recharge occurs. When the precipitationevent ceases after 10 days, continuing evaporation createsa soil moisture deficit precluding any further recharge. Asthe soil moisture deficit (depth to saturation) increases,the actual evaporation rate drops below the potential rate,

Figure 5. Model response to a 10 day, 20 mm d�1 rainfall event. In thisexample the infiltration capacity was set at 20 mm d�1, so no runoffoccurs. Potential recharge starts once the soil is completely saturated andstops immediately a soil moisture deficit is initiated. Actual evaporation

declines as the soil moisture deficit increases



and so both actual evaporation and soil moisture contentslowly decline until the next precipitation event. In theabsence of further precipitation the extinction depth forevaporation is closely approached (to within 10 mm) aftera period of almost three years.

THE LINZOR BASINS AS AN EXAMPLE

Hydrogeology

The Linzor Basins lie at high altitude (4000–5600 m)in the Rıo Loa catchment at 22Ð2 °S (Figure 6). Thebasins are dominated by Quaternary strato-volcanoescomposed of andesitic to basaltic lavas, breccias andavalanche deposits, inter-digitating with andesitic todacitic tuffs and ashes that extend up to 10 km fromthe volcanoes as skirts (Marinovic and Lahsen, 1984).Small areas of the catchments have been glaciated andPleistocene lateral and terminal moraines occur (Holling-worth and Guest, 1967). These Quaternary volcanicsare sourced from vents that punch through considerablethicknesses of Miocene-Pliocene volcanic and sedimen-tary strata.

Several large, perennial springs discharge from perme-able Quaternary tephra overlying relatively impermeableMio-Pliocene volcanics. These springs form the prin-cipal sources of the Rıos Toconce and Hojalar, whichdrain the two basins. Another perennial spring at 4550 mand several seasonal springs discharge from the base ofthe eastern volcanoes. During some wet seasons surfacewater flows along the full length of watercourses connect-ing the higher springs to the lower. The highest, easternparts of the basins form the main surface water dividebetween the Andean west slope and the internally drainedAltiplano.

Flows from the springs and the streams were measuredduring the dry (August 2000) and wet (February 2001)seasons (Figure 7) and sampled for their hydrochemistry(see Supporting Information). The temperature of thewaters emanating from the base of the Quaternary tephrais significantly higher (23Ð3 š 1Ð5 °C) than that fromthe foot of the volcanoes and moraines (10Ð3 š 1Ð7 °C).Similarly, during the dry season, the chloride content isalso lower from the upper spring (12 mg l�1) comparedwith the lower spring samples (119 š 53 mg l�1). Also,the chloride content tends to drop during the wet seasonfrom 119 š 53 to 93 š 11 mg l�1 for the lower springs.

The weighted mean value of Cl in precipitation for thecentral Andes has been estimated at 6Ð3 mg l�1 (Hous-ton, 2007), and although this value is high by worldwidestandards, it is explicable as a result of atmospheric con-centration in the west Andean rainshadow (see Support-ing Information). Based on this value, the CMB tech-nique can be used to estimate mean annual recharge(Figure 7). For the Toconce catchment the lower springsindicate 11Ð8 š 0Ð4 mm a�1 (7% of precipitation) risingto 116 mm a�1 (an estimated 53% of precipitation) at theupper spring. The lower springs in the Hojalar catchmentindicate 7Ð7 š 2Ð9 mm a�1 recharge (5% of precipitation)although this may be reduced due to Cl sources other thanprecipitation.

Enriched 3H counts (detection limit 0Ð1 TU) were madeby the University of Waterloo, Canada, and the Insti-tute of Geological and Nuclear Science, New Zealand(Figure 7). Mean residence times (MRT), estimated forthe samples using the methodology of Houston (2007),indicate short residency with the upper spring discharg-ing essentially fresh precipitation, and the lower samplesa residency of 18–27 years. The longer MRT in theHojalar basin is consistent with higher Cl values indi-cating greater rock–water interaction.

Figure 6. Hydrogeological map of the Linzor catchments, showing principal surface water features and groundwater discharge sites (springs)


2390 J. HOUSTON

Figure 7. Flow regime and hydrochemistry of the Linzor catchments. Flow rates and sampling were conducted in August 2000 (dry season) andJanuary 2001 (wet season). Chloride mass balance (CMB) recharge is based on wet season 2000 weighted mean Cl in rainfall (6Ð3 mg l�1), meanprecipitation at Linzor (164 mm) and estimated precipitation for the upper spring site (220 mm). Mean residence time (MRT) calculated using the

data in Houston (2007)

Taken together, the hydrogeological and hydrochemi-cal data suggest that the upper springs are sourced by pre-cipitation infiltrated into the volcanic cones and morainesthat have minor storage capacities and either dischargerapidly at ambient temperatures or possibly transfer waterto deeper levels. The water discharging from the lowervolcanic tephra is distinct, and suggests a larger, morepermanent storage capacity to maintain discharge dur-ing the dry season. Temperatures in the lower volcanictephra indicate a high geothermal gradient with greaterrock–water interaction, especially in the Hojalar catch-ment. This is consistent with the occurrence 10 km tothe south, of the geothermal field of El Tatio, which dis-charges up to 0Ð5 m3 s�1 water at 86 °C (Lahsen and Tru-jillo, 1976), indicating the presence of high geothermalgradients in the area. Residence times are still relativelylow however, confirming that recharge is occurring on aregular basis.

Thus, the Linzor catchments represent an ideal localityto test the veracity of the recharge model.

Model inputs, results and checks

The recharge model for the Linzor Basins assumesa two-layer basin; 4100–4500 m and over 4500 m.Greater elevational subdivision is possible but given thelimitation of input data to Linzor at 4096 m, this is notconsidered warranted. Daily rainfall and pan evaporationdata are missing 5Ð3% and 14Ð4% data respectively,during the 26-year period from 1977 to 2002. Meandaily data have been inserted in these gaps for modellingpurposes and are not considered likely to impact theresults significantly. The greater number of missingevaporation data is less important since year-on-yearvariations are significantly less than for rainfall. Rainfalland pan evaporation data from Linzor are assumed tobe applicable to the whole of the lower layer, whilst for

the upper layer, Linzor data has been factored by theelevational relationships described above. The factors forrainfall and pan evaporation are 1Ð3 and 0Ð88 respectively,giving mean annual values of 221 and 1709 mm a�1

at 4500 m, which are reasonable by comparison withhigh-level data from elsewhere in the central Andes.This synthetic data is then applied to the whole areaabove 4500 m. Using the data for the lowest levelin each layer will result in conservative estimates forrecharge.

Infiltration capacity for each layer was estimated fromthe areally weighted values determined for each soil typeresulting in 21Ð6 and 22Ð4 mm d�1 for the lower andupper layers respectively (Table II). The field capacitywas similarly estimated as 0Ð1, based on the areallyweighted d50 values (0Ð4 mm) and the chart in theSupporting Information.

Daily measured rainfall and pan evaporation from Lin-zor are used as input to the model (Figure 8). Notethat precipitation is largely limited to the summer periodJanuary–March and is highly variable year on year. Max-imum daily intensities typically vary between 20 and50 mm. During the 26-year period wet years tend to

Table II. Calculation of areally weighted infiltration rate for thetwo subareas of the Linzor basins model

Soil Infiltration rate 4100 m 4500 m

mmd�1

area(%)

mmd�1

area(%)

mmd�1

Moraine 121 1Ð0 1Ð21 10Ð0 12Ð10Tephra 27 73Ð0 19Ð71 26Ð5 7Ð16Lava 5 14Ð0 0Ð70 63Ð5 3Ð18Ignimbrite 0Ð21 12Ð0 0Ð03 0Ð0 0Ð00

Weighted infiltration rate 100 21Ð6 100 22Ð4



Figure 8. Model results for recharge to the Linzor basins (1977–2002). Top panel shows input daily precipitation and pan evaporation measured atLinzor (4096 m). Second panel shows calculated soil moisture content and actual evaporation for the 4100 m layer. The third shows the output fromthe two-layer model; daily recharge (compared with La Nina events). Bottom panel shows a check between model output runoff and downstream

adjusted observed flows. See text for discussion

cluster together (1984–1987 and 1997–2001) and areassociated with La Nina (Houston, 2006a). Despite LaNina conditions being established during only 23% ofthe period, these periods account for 42% of the precipi-tation. Daily pan evaporation is quite variable, but thereis a regular annual cycle related to temperature (Houston,2006b) that varies little from year-to-year. Pan evapora-tion rates typically vary between a winter low of 2–5 mmd�1 to a summer high of 7–10 mm d�1, allowing ampleopportunity for summer runoff and recharge to occur.Peak evaporation rates usually occur in December, justprior to the main rainfall period of January–March. Aregression of daily rainfall against daily pan evaporationfor the months of January–March (see Supporting Infor-mation) suggests a negative relationship confirming thatwet, cool, cloudy weather reduces evaporation allowingenhanced opportunity for runoff and recharge.

During a typical annual cycle the soil moisture contentis at a maximum, and the equivalent depth to saturationat a minimum during the wet season, with a gradualdecline in soil moisture content, and increase in depthto saturation during the dry season. Typical deficits atthe end of the dry season are 90–110 mm at 4100 m(80–100 mm at 4500 m), and vary little year on year.Conversely, soil moisture contents during the wet seasonare highly variable, dependent on the intensity andduration of the precipitation. As a result of the soilmoisture deficit that exists throughout most of the year,evaporation is curtailed except during those periods when

infiltration provides adequate moisture for evaporation tooccur at, or close to the potential rate.

Recharge only occurs once the soil is at field capacityand the equivalent depth to saturation is zero, as dictatedby the model. Recharge is restricted to a total of 50 daysin 12 years at 4100 m (107 days in 13 years at 4500 m)during the 26-year period. As expected daily rechargeamounts are highly variable achieving a maximum of20 mm at 4100 m (22 mm at 4500 m). For the LinzorBasins the model calculates the overall mean annualrecharge as 28 mm a�1, or 7Ð4 million m3 a�1.

How realistic is this result? Table III shows a com-parison of model results with those determined by theCMB method both regionally (Houston, 2007) and locally(this study). The regional study found that mean annualrecharge in mm (RE) varied with elevation according to:

RE D 0Ð0001 e�0Ð0029A�

Table III. Mean annual recharge (in mm) calculated by the modelfor each layer and combined, compared with mean annualrecharge calculated from regional CMB data (Houston, 2007)

and spot data within the Linzor basins (see Figure 7)

Model Regional CMB Local CMB

4100 m 15Ð1 14Ð6 10Ð4 š 2Ð54500 m 36Ð4 46Ð5 115Ð5Combined 28Ð1 29Ð6 25Ð4 š 40


2392 J. HOUSTON

At Linzor (ca. 4100 m) mean annual recharge from themodel is 15Ð1 mm, 3% greater than the regional CMBand 44% more than the average spot results for the lowersprings in the Toconce and Hojalar catchments. For thesynthetic data at 4500 m the model result is 22% lessthan the regional, and 67% less than the spot CMBresults. The combined result for the two-layer model is5% less than the regional CMB estimate and 9% morethan the combined spot results for the upper and lowersprings. These results suggest that the model performsless well using synthetic data (the 4500 m layer) ratherthan real data (4100 m layer). Perhaps unsurprisingly,spot estimates of recharge using CMB method are morevariable than regional estimates, so the model performsless favourably in comparison with spot results ratherthan regional. However, overall the model performs verywell and differences of 5–9% between different estimatesof recharge are much smaller than typically found incomparable studies.

As a further independent check, modelled overlandflow or flood runoff may be compared with the gaugedflow in the Rıo Salado at El Sifon, ca. 30 km downstreamfrom Linzor. At this point the Rıo Salado incorporatesnot only the Rıos Toconce and Hojalar but also severalother tributaries. At the same time, licensed abstractionsamounting to a total of 0Ð99 m3 s�1 mean that direct com-parison of the flows cannot be made. By converting tospecific runoff (mm d�1) and making some adjustmentsfor catchment elevation and runoff characteristics com-pared with the Linzor basins, the form of the hydrographis preserved (Figure 8, lower panel), and may be usedto verify the general magnitude and frequency of floodevents generated by the model. No attempt is made inthe model to allow for groundwater discharge from theaquifers, so that baseflow is not represented. However,it is clear that the modelled runoff captures the knownflood events rather well.

Based on a comparison of model recharge results withthe CMB technique and model flood flows with observedflood flows, the model (algorithms and an example areprovided in the Supporting Information) is considered toprovide a robust and reliable representation of diffusegroundwater recharge.

RECHARGE CHARACTERISTICS OF HIGHALTITUDE, ARID ANDEAN AQUIFERS INFERRED

FROM THE MODEL

The model only simulates diffuse groundwater rechargeand does not account for other sources of recharge such asmountain front recharge through alluvial fans (Houston,2002), nor ephemeral stream channel losses (Houston,2005). Diffuse recharge increases with elevation and isfavoured by the coarse-grained immature soils lacking invegetation over 4000 m altitude.

Diffuse recharge is not an annual phenomenon in thisenvironment as a result of the extreme variability inprecipitation. Recharge occurs, on average, in half of all

years, but tends to group into runs of wet years and 62%of all recharge is concentrated into La Nina episodes thatoccur in only 23% of years.

The relationship between recharge and rainfall (Figure9) indicates that no recharge occurs when annual pre-cipitation is less than ca. 120 mm a�1. This is in agree-ment with worldwide data from a variety of environments(Scanlon et al., 2006). Over 120 mm a�1 there is a sig-nificant relationship between recharge and precipitation:

RE D 0Ð44 RF � 52Ð5

Frequency analysis of the modelled recharge indicatesthat 50 mm a�1 has a return period of 3 years and100 mm a�1, 10 years.

The model suggests little difference in antecedent soilmoisture deficits between years with and without recharge( D �3Ð3 mm). Antecedent soil moisture seems to beless important in controlling recharge than runoff (cf.Houston, 2005), probably because the long duration ofthe dry season generates an equalizing effect. On thecontrary, mean annual actual evaporation is much higherin years with recharge (210 mm) than in years withoutrecharge (94 mm) due to the greater availability of soilmoisture as a result of higher precipitation. Both rain-fall intensity ( D C101%) and the number of rain-days( D C23%) are greater in years with recharge. Thus,both precipitation intensity and its cumulative summeramount would appear to be the main factors controllingnot only recharge but also increased evaporation, whilstdirect runoff is dependent on antecedent soil moisture aswell. In turn, daily and seasonal precipitation character-istics are strongly influenced by convective activity andENSO at the meso- and synoptic scales respectively.

These results provide greater insight into the spatialand temporal variability of diffuse high altitude, Andeanrecharge and its long-term control by environmental andclimatic variations. The model allows a more refinedrepresentation than currently widely used techniques, andits application to other sites will likely benefit waterresource studies, allow further enhancements to be madeand add to the knowledge of Andean hydrology.

Figure 9. Modeled recharge versus annual precipitation for the Linzorbasins



ACKNOWLEDGEMENTS

This article benefited from discussions with C. Latorreat Universidad Catolica de Chile. Nazca S.A. providedthe funding for this study. The meteorological andhydrological data were supplied by the Direccion Generalde Aguas, Santiago.

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a recharge model for high altitude, arid, andean aquifers

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