Cold regions hydrology, snow, and PUB

Transcription

1 Preditions in Ungauged Basins: PUB Kik-o (Proeedings o the PUB Kik-o meeting held in Brasilia, 2 22 November 22). IAH Publ. 39, Cold regions hydrology, snow, and PUB JOHN POMEROY Centre or Hydrology, University o askathewan, askatoon, askathewan 7N 5C8 Canada and Institute o Geography & Earth ienes, University o Wales, Aberystwyth Y23 3DB, Wales, UK pomeroy@usask.a Abstrat Cold regions hydrology has a great demand or improved predition beause most old regions are notoriously ungauged and beause the old regions hydrologial yle has some uniquely important omponents related to the solid phase o water. For instane, snow aumulation ontrols water balane and peak streamlow in many old region athments. However, the quantity o snow aumulated in orested athments is oten very unertain beause snow measurements are usually taken in small learings. Aumulation o snow under orest anopies delines with inreasing anopy density and lea area beause o snow intereption and sublimation in the anopy. easonal snow aumulation measurements olleted over a deade rom various orest stands in western Canada were used to test and develop methods to relate orest snow aumulation to stand properties and observations o either small learing seasonal snow aumulation or seasonal snowall. At the stand-sale, physially-based snow intereption equations predited seasonal snow aumulation rom the stand lea area and the seasonal snow aumulation or snowall in adjaent learings. A simple parametri orm o these equations showed the sensitivity o seasonal snow aumulation to lea area at the orest stand sale and suggested a relationship to extrapolate snow aumulation or snowall measurements rom learings to orests. Lea area an be easily quantiied rom remote sensing imagery and so this tehnique is suited to ungauged basins. Key words old regions hydrology; orest snow; intereption; PUB; snow aumulation; snow hydrology INTRODUCTION The development o sientii hydrology is permitting preditions o water system behaviour that rely to an inreasing degree on proesses as desribed by hydrologial priniples. Prediting land surae proesses, streamlow and snow and ie reserves in ungauged areas has partiular relevane to the needs o old regions hydrology and the dynamis o snow and ie systems. Observational networks o snowall, snow water equivalent, glaier mass balane, ie extent, and streamlow have always been oarse in old regions, and reently have delined dramatially. For instane, operational monitoring o disharge rom the glaial, mountain, boreal, sub-arti and arti zones to the Arti Oean has delined by at least 4% in the last 15 years; beore this deline, 35 5% o disharge to the Arti Oean was rom ungauged basins. The diiulties o measuring areal snow aumulation, rozen soil moisture ontent, glaier mass balane and streamlow under ie and during ie break-up mean that even routinely gauged basins represent areas o high unertainty in hydrologial alibration and estimation. Beause o a long-standing problem o data availability in old Copyright 27 IAH Press

2 86 John Pomeroy regions, there is a tradition o applying physially-based preditions based on hydrologial proesses and remotely sensed data to large-sale systems; the approahes may also have relevane to more temperate hydrologial appliations. Given urrent estimates that global warming impats on hydrology will be most evident in the ontinental high latitudes, the reognition o the key inluene o reshwater on northern oean irulation and hene global limate, the partiularly strong link between old regions hydrology and eosystem dynamis and the strong reliane o northern aboriginal peoples on water-based subsistene liestyles, the negleted 4th world o the old regions will be an issue o some importane that PUB should apply a distintive eort to. Both water balane and peak runo in old regions are strongly inluened by snow aumulation over the athment. now survey networks in representative loations have delined dramatially in most ountries and oreasters now must oten rely on point measurements o snow depth rom an automated meteorologial station or remote observations o snow water equivalent made rom open terrain or gaps in orest anopies. This is partiularly serious in the irumpolar boreal orest, whih oupies roughly 16% o the ontinental area o the Earth. A better understanding o the relationship between the snow aumulation observed in small learings and the aumulation in adjaent orested environments an assist in prediting athmentwide snow water equivalent. The purpose o this paper is to outline a simple theory or extrapolation o snow aumulation estimates rom where they are gauged to where they are ungauged in a northern orest environment. THEORY Presuming horizontal redistribution is negligible, over a snowall event (period o snowall) intereption, i, is deined as that snowall whih does not reah the ground. I the snowall, p, into a learing is the same as that to the top o a orest anopy, then: p p i (1) = where p is the sub-anopy snowall or some event. The intereption term deined in equation (1) was the subjet o theoretial and observational study by Hedstrom & Pomeroy (1998). They disussed results in terms o intereption eiieny, i/p = e i, whih was alulated rom a physially-based ormulation. The snow intereption ormulation o Hedstrom & Pomeroy (1998) relates intereption to lea area index, tree speies, anopy density, air temperature, wind speed and snowall. For a single snowall event into a snow-ree anopy, Hedstrom & Pomeroy s algorithm an be simpliied to its primary ators, as: C p = 5.8LAI ' i 3.94 LAI' 1 e (2) where p is above-anopy snowall during the intereption event, eetive winter lea area index, LAI, is the total horizontal area o stems, needles and leaves per unit area o ground, C is anopy density and the units are mm or the oeiients 3.94 and 5.8,

3 Cold regions hydrology, snow, and PUB 87 p and i. Hedstrom & Pomeroy s intereption algorithm traked snow load in the anopy; however equation (2) is only valid or single snowall events. For every inrement o p, equation (2) assumes that all interepted snow is retained as anopy snow load rom the previous inrement. The assumption that snow load is preserved over the time between snowall inrements is only likely to be valid during individual snowalls and or short periods aterwards. Interepted snow eventually sublimates, unloads or drips to the ground. Over a winter season it may be presumed that this has ourred. easonal sublimation E may then be ound as: P P U D E (3) = where P denotes seasonal snowall (subsripts and reer, as beore, to that o a learing and sub-anopy, respetively), U, unloading and D, drip and the seasonal sum o intereption, i = E + U + D. Presuming that redistribution, surae melt and surae evaporation are negligible, the mass balane equations or the orest and learing redue to = P and = P U D, resulting in: = E (4) The sublimation term E was the subjet o investigation by Pomeroy et al. (1998) and requires the solution o oupled mass and energy balane equations. A sublimation eiieny term, e s, may be deined as E/ i. This eiieny is expeted to be lower in humid temperate winter environments where in-anopy melt and unloading o wet snow rom the anopy are large (e.g. Lundberg et al., 1998; tork & Lettenmaier, 1999) and higher in old dry environments where sublimation proesses may proeed with relatively little hindrane (Pomeroy et al., 1998; Parviainen & Pomeroy, 2). It is also expeted to vary with several other ators suh as snow age, amount o interepted snow, branh elastiity, wind and radiation penetration into the anopy, and anopy struture. Using the sublimation and intereption eiienies then equation (5) may be expressed as: i = esei = (1 es ) (5) p where the eiienies e i = i / or i = e i and e s = E / i or E = e s i, must be evaluated rom the same data set and or the same time interval. It is assumed that the seasonal eiienies an be approximated by the means o the ratios i / P (sine P ) and E / i, or shorter time periods or whih equation (2) is valid, e.g.: i P easonal i P Monthly i P Weekly et By summing event-based intereption rom intervals or whih it an be assumed that the anopy has beome initially snow-ree, equation (2) an be employed. The intereption eiieny term may be summed to seasonal terms (the seasonal value (6)

4 88 John Pomeroy being the summation o event intereption eiienies) as e i = i/. With this presumption, equation (2) with its event-based (roughly weekly) time sale an be ombined with equation (5) to provide: = CPj 5.8LAI ' 3.94LAI ' 1 e 1 e s (7) Pj where P j is the snowall into a learing over snowall event time interval j. Equation (7) provides a means o alulating seasonal snow aumulation in a orest, based on aumulation in a learing, the sublimation eiieny, the magnitude o individual snowall events, anopy density, and winter lea area index. It is presumed that the anopy beomes snow-ree over time interval j, thereore some estimate o snowall amount over time interval j must be made. Field observations now depth and density surveys were onduted during the snow season (usually Otober to April) in the Canadian boreal orest rom 1993 to 22, on a weekly basis in the Prine Albert Model Forest, askathewan (PAMF) and on a monthly basis at Wol Creek Researh Basin, Yukon. Timing o surveys was sometimes varied slightly to apture a snowall event or antiipate a melt period, but was onstrained by the operational requirements o the study programmes in the respetive areas. REULT Over all stands, seasonal learing snow aumulation varied rom 54 to 124 mm and stand-sale seasonal orest snow aumulation varied rom 28 to 11 mm water equivalent with means o 86 and 59 mm or learing and orested landsapes, respetively. The ratio o orest to learing snow aumulation / delined rom values near 1. to near.5 as lea area index, LAI and anopy density, C, rose rom.2 to 4.1 and.95, respetively, as shown in Fig. 1(a),(b). The ratio / was negatively orrelated to LAI and C with oeiients o.69 and.72, respetively. To implement equation (7) the magnitude o p must be ound and the behaviour o the sublimation eiieny, e s, determined. It is proposed that or the boreal orest, the reommendation o Hedstrom (1998) is ollowed and that weekly snowall be used to estimate p. Over three seasons ( ) at PAMF or whih weekly data quality was highest, the mean weekly winter period snowall into a learing was 5.1 mm. Mean monthly winter period snowall at Whitehorse was 2.4 mm over our seasons ( ), providing a weekly mean o 4.8 mm. A value or p o 5 mm was thereore adopted or subsequent analysis. olving or e s rom equation (7) and measurements provided a mean e s o.72 with a standard deviation o.32. There were no trends o e s with lea area index or learing snow aumulation.

5 Cold regions hydrology, snow, and PUB 89 (a) / LAI' (b) 1.8 / Canopy Density Fig. 1 Ratio o orest to learing snow aumulation as a untion o stand harateristis: (a) lea area index (eetive winter), (b) anopy density (winter). A omparison o equation (9) using p = 5 and e s =.72 with measurements is given in Fig. 2, with a R 2 o.8, mean dierene (measured modelled) o.48 mm and a standard deviation o dierenes o 9.4 mm. Predited Forest now Aumulation Measured Forest Aumulation Fig. 2 Points indiating measured seasonal orest snow aumulation (mm) and that predited using equation (9) using snowall event size, p, o 5 mm and sublimation eiieny, e s, o.72 and a 1:1 line or reerene. 12 DICUION Equation (7), though linked to intereption theory, is relatively omplex or predition and upsaling purposes. An examination o the sensitivity o intereption eiieny e i to LAI an provide a simpler orm. The itted logarithmi orm is:

6 9 John Pomeroy e i =.1984 ln( LAI ') +.39 (8) whih has a R 2 o.99 when ompared to the ull physially based equation. From equations (5) and (8) a parametri equation to predit snow aumulation in orests based on that in learings and lea area index is thereore: = ( 1 es (.2ln( LAI ') +.31)) (9) Equation (9) has a mean dierene with measurements o 1.24 mm, standard deviation o dierenes o 9.72 and a R 2 o.79 (Fig. 3). Assuming the sublimation eiieny is.72, then this equation beomes: [ 1 (.144 ln( ') +.223) ] = LAI (1) Equation (1) is reommended or extrapolation o either measurements o snow aumulation on the ground in small learings or seasonal snowall, to adjaent orested regions. The degree o unertainty inreases with requeny o mid-winter melt and wind redistribution o snow rom the learing, but the equation appears to work well in the boreal orest o western Canada. Lea area index an be estimated rom remote sensing imagery and onverted to the eetive lea area index used in the parametri equation (equation (1)). The other input,, an be derived rom snowall estimates rom meteorologial models, measurements or snow depth estimates in a small learing. As standard meteorologial stations or weather oreasting, limate monitoring and orest ire predition are loated in small learings, this permits the use o a wider range o data sets or old regions orest streamlow predition and is partiularly useul where snow aumulation is not measured. Predited Forest now Aumulation Measured Forest Aumulation Fig. 3 Perormane o the parametri orest snow aumulation equation (equation (9)) presuming that sublimation eiieny is.72; measured and modelled aumulation (mm) as points with a 1:1 line or omparison. CONCLUION easonal snow aumulation in orests at the stand sale is shown to sale with lea area index ollowing the intereption theory o Hedstrom & Pomeroy (1998); the untion is one o delining aumulation with inreasing lea area. It is antiipated

7 Cold regions hydrology, snow, and PUB 91 that the assumptions underlying this relationship are valid where mid-winter melts, wind redistribution and surae evaporation are inrequent or small. Knowledge o snow water equivalent at a point or an estimate o snowall and the spatial distribution o lea area index in a athment an thereore provide the distribution o snow aumulation. This relationship will permit enhaned preditions o the snow reserves available or melt in densely orested areas where they annot be measured. REFERENCE Hedstrom, N. R. (1998) Development and Evaluation o a Cold Regions now Intereption Model. Master o iene Thesis. Department o Agriultural and Bioresoure Engineering, University o askathewan: askatoon, Canada. Hedstrom, N. R. & Pomeroy, J. W. (1998) Measurements and modelling o snow intereption in the boreal orest. Hydrol. Proesses 12, Lundberg, A, Calder, I. & Harding, R. (1998) Evaporation o interepted snow: measurements and modelling. J. Hydrol. 26, Parviainen, J. & Pomeroy, J. W. (2) Multiple-sale modelling o orest snow sublimation: initial indings. Hydrol. Proesses 14, Pomeroy, J. W., Parviainen, J., Hedstrom, N. R. & Gray, D. M. (1998) Coupled modelling o orest snow intereption and sublimation. Hydrol. Proesses 12, tork, P. & Lettenmaier, D. P. (1999) Prediting the eet o orest anopy on ground snow pak aumulation and ablation in maritime limates. Proeedings o the Western now Conerene 67, 1 12.