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Instrumentation System to record distribution profile of Snow Layer Temperature for modelling of Snow Avalanche Forecast
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Instrumentation System to record distribution profile of Snow Layer Temperature for modelling of Snow Avalanche Forecast


The measurement of snow hydrological parameters is extremely important in developing a model for the predication of Snow avalanche as well as Snowmelt water in the rivers. When direct measurement of …

The measurement of snow hydrological parameters is extremely important in developing a model for the predication of Snow avalanche as well as Snowmelt water in the rivers. When direct measurement of these parameters is practically difficult, its dependence on snow temperature is used to develop snow cover models. A robust model for avalanche forecasting requires a sophisticated instrumentation system which can measure the required temperature parameters at right data points within snow pack. A Snow Temperature Profile Sensing System along with Surface temperature Sensor has been designed to measure Snow temperature gradient, temperature distributions, and average temperature of snow pack, snow surface, ground and air. This paper describes the theoretical background to identify right temperature parameters needed to be measured and present a unique design approach to develop a measurement system to measure snow temperature at various points to provide an integrated data for forecasting model.

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  • 1. R. Attri Instrumentation Design Series (Snow Hydrology), Paper No. 1, August 1999Design of an Instrumentation System to record distributionprofile of Snow Layer Temperature for modelling of SnowAvalanche ForecastRAMAN K. ATTRIEx-scientist (Geo-scientific instrumentation), Central Scientific Instruments Organization Indiarkattri@rediffmail.comABSTRACT: The measurement of snow hydrological parameters is extremely important in developing a model for thepredication of Snow avalanche as well as Snowmelt water in the rivers. When direct measurement of these parameters ispractically difficult, its dependence on snow temperature is used to develop snow cover models. A robust model for avalancheforecasting requires a sophisticated instrumentation system which can measure the required temperature parameters at right datapoints within snow pack. A Snow Temperature Profile Sensing System along with Surface temperature Sensor has been designedto measure Snow temperature gradient, temperature distributions, and average temperature of snow pack, snow surface, groundand air. This paper describes the theoretical background to identify right temperature parameters needed to be measured andpresent a unique design approach to develop a measurement system to measure snow temperature at various points to provide anintegrated data for forecasting model.1. INTRODUCTIONThe snow manifests climatic changes, potential release ofavalanches, river run off water, glacier sliding and relatedphenomenon in the mountain areas and planes nearby. Thesnow hydrological parameters and its dependence on otherenvironmental factors govern the risk of snow avalanche andamount of water melting down the rivers (Yamazaki et al.,1993). Among all the environment factors, temperatureparameters have direct impact on risk of snow avalanche. Ithas been found that stability, strength and structure ofdifferent layers composing snow pack mainly depends upontemperature distributions within and outside snow pack(Colbeck, 1989). If these temperature distributions areknown, hydrologist can develop a forecasting model for snowavalanche and generate a man-kind safety alarming system.However, design of such alarming and forecasting systemdepends mainly on how accurately the right temperaturevariables are measured by an instrumentation system. Theaccuracy of snow cover avalanche forecasting model dependsupon selection of right temperature variables and right datapoints.Researchers have developed a mathematical energymodel of the snow cover (Singh, 1994; Yamazaki et al.,1993; Anderson, 1976). The major issue is to identify theright set of temperature parameters required for measurementand translating those variables into a feasible instrumentationsystem. In this paper, we have described the approach toidentify the various temperature parameters required to bemeasured to develop snow cover avalanche forecast modeland approach to design an instrumentation system to measurethose parameters in physical form. Major focus of the paperis on how an instrumentation system can be design based onenergy balance model of snow cover developed by Anderson(1976), Bader & Wielenmann (1992) and Singh (1994).2. THEORETICAL BACKGROUNDSnow being a thermodynamically unstable materialundergoes morphological changes such as crystal growth,change in density and internal weight pressure, percolation ofsnow melt water etc within the snow pack because of heatexchange at snow surface, ground interface and at airinterface (Satyawali, 1994).Many researchers established that thesemorphological changes in the snow inherently depend uponthe temperature parameters like - Snow layers temperaturegradient, Average Temperature of Snow pack, Snow surfaceTemperature, Ground interface temperature and True airinterface temperature (Schwerdtfeger, 1962).Literature shows two approaches in establishingsnow properties with temperature parameters:2.1 Approach 1: Dependence of snow properties ontemperatures parametersThe first temperature dependence of snow crystal growth ontemperature has been shown by Mellor (1977) according towhich rate of morphism of crystals J is dependent upon thetemperature gradient as well as snow surface temperaturegiven by following equation.J = - {(N D P L) / (RT)} {∂T/ ∂z} …. (1)The formations of snow cover take place with thedevelopment of different forms of crystals whose shape, size,bonding and packing controls the mechanical properties,stability and strength of snow cover thus evolved (Colbeck,1989). Rate of this crystal growth is given do = J/ρ where ρis the ice density (0.917 gm/cm3. Using expression from
  • 2. R. Attri Instrumentation Design Series (Electronics), Paper No. 1, January 20002 | Copyright © 2000 Raman K. Attriequation (1), the resultant crystal grown as a result of thevapour deposition is given by:d = di + M/T {∂T/ ∂z} .... (2)Where M is a constant. The expression (2) showsthat the final snow growth is directly proportional totemperature gradient & inversely proportional to Snowsurface temperature.Further, density and hence, snow bound mass is alsorelated to this crystal growth which in turn depends upontemperature gradient of different layers. Snow bound mass iskey component causing snow avalanche when excessivesnow mass breaks the ground-snow bond underneath (Bader& Wielenmann, 1992). According to Mellor (1977) change insnow density is exponentially dependent upon average snowlayer temperature:Δρ = A ρ Exp (-B ρ) Exp (-0.08(273- Ts)) P Δt …. (3)Where A and B are constants, ρ is the Initial snowdensity (g/cm3), Ts is the average snow layer temperature inKelvin, P is the over burden pressure and Δt is the timeinterval in hoursAlso, snowmelt is dependent upon the temperaturedistribution inside and above the snow. The study andforecasting of snow melt water is necessary to forecast wetsnow avalanche. The snow melt produces some free water,the movement of this water vertically downward increasesthe rate of metamorphism, reduces mechanical strength anddeformation resistance of snow pack by weakening inter-granular bonds (Anderson, 1976). With the increase in freewater content, the snow tends to lose cohesion and inter-granular bonds start to disintegrate. This causes drasticdecrease in shear strength and hence wet snow avalanche.The volumes of melt water production for a given inputapproximately directly proportional to the snow-covered areaand the temperature. Hall (1985) states that energy input isfrequently represented by degree-day factor and melt watervolume is calculated as follows:Vm = a T A …. (4)Where Vm is the melt-water volume in meter cubes,a is the degree-day factor, T is the number of degree days, Ais the snow covered area in meter squares.Above evidences lead to conclusion that snowsurface temperature along with snow layer temperaturedistribution is very important parameter needed for snowavalanche and flood run-off water forecast model.2.2 Approach 2: Dependence of heat exchanges onsnow cover on temperature parametersIt has been found by many researchers like Mellor (1977),Colbeck (1989), Anderson (1976) and Jordan (1991) that thestability, strength and other properties of snow is mainlyrelated with the net exchange in at snow-air interface, snow-ground-interface and snow pack itself. The energy at thesnow-air interface is considered to deduce the surface melt,energy exchange at the snow-ground interface examines thepossibility of destruction of bond between the ground and thesnow-pack. Net gains in energy, which is directional additionof various energies at both the interfaces, satisfy the coldcontent, conduct through the snow pack and affect melt(Singh, 1994). A measurement of this energy enableshydrologists to make a snow pack behavioural model andhence develop an avalanche forecast model. These energiescan be computed if physical parameters of snow surfacetemperature, temperature gradient etc is known.Singh (1994) presented a snow cover model anddepicted various energies invading on snow cover from air-snow interface as well as snow-ground interface in fig [1].Snow-air boundary is being invaded by radiation energy Qr(radiation flux) from above. Most of the energy at the snow-air interface Qs (sensible heat flux) is used in satisfying coldcontent and changing the temperature of top layer, some ofthe energy Ql (Latent heat flux) produces melt at snow-surface, rest of the energy is used in conduction at surfaceand absorption in interior layers.Fig. 1: Theoretical depiction of Snow Cover Model andsurface energy exchanges at Snow-Air interface and snow-ground interface. An exchange of radiative energy as Short-wave and long-wave occurs at snow-air interface into thesnow surface and out of snow surface. Sensible heat isabsorbed which results in melting of snow surface. Latentheat flux represents the energy used to melt F amount ofsnow at a depth of Z.Singh (1994) derived energy balance equation atsnow surface governing the change in snow temperature asunder:Net Energy ΔQ = Radiation Energy Qr + Sensible Heat Ql +Latent Heat Qs …. (5)Where ΔQ is the Net Energy Invading the SnowSurface, Qr (radiation flux) is the radiation energy comingtoward surface, Qs (Sensible heat flux) energy at the snow-airinterface, Ql (Latent heat flux) energy used in producing themelt.
  • 3. R. Attri Instrumentation Design Series (Electronics), Paper No. 1, January 20003 | Copyright © 2000 Raman K. AttriSensible heat Qs is sum of the two energycomponents namely the energy used in raising snow temp ofsnow depth Z and energy conducted into the snow surface.On the other hand Latent heat is energy used in melting Famount of the snow of depth Z.Above equation is expanded as under which iscalled snow-air interface energy balance equation:ΔQ = ε σ M [0.76Ta4–Ts4] + Cs ρs{dTs/dt} dz +λs{∂Ts/∂z}snow surface+ Lf F dz …. (6)Where Ta is ambient temperature in Kelvin, Ts issnow surface temperature in Kelvin, M is the constant ofequation, Cs is the Specific heat of snow, ρs is Snow density,dTs is the change in snow temperature produced, z is theSnow depth, λs is the thermal conductivity of snow, ∂Ts/∂z isthe temperature gradient in snow pack, Lf is the latent heat offusion of snow, F is the amount of snow melt per unit timeand unit volume.This is the basic equation which implies the directdependence of energy exchange and hence meteorologicalinteraction of snow related to its temperature factors.Andersan (1976) and Ono et al. (1980) have furthercomputed these individual terms in terms of Snow surfaceand Air temperature etc. In the above equations, effects of allother parameters have not been included to keep thediscussion to temperature distribution studies.Schwerdtfeger (1962) proposed a Fourier one-dimensional heat conduction equation for snow cover whichdepicts heat conduction along depth of snow Z as under:Sensible heat flux at snow-ground interface Cs ρs {∂T/∂t} =heat flux in ground λs {∂2T/∂z2} …. (7)Above expressions establishes following conclusions:-(1) Radiative energy is function of snow surface temperatureand temperature gradient of the snow pack.(2) Sensible heat is dependent on temperature gradient of thesnow pack as well as time variation of the temperature(3) Latent heat is dependent on the snow cover thickness(4) Energy conducted within snow is dependent ontemperature gradientIt has been established that if we could measurefollowing key parameters, we can directly compute aboveenergies and hence the other interdependent properties ofsnow (Ganju, 1994).• Ambient temperature Ta• Snow surface temperature Ts• Temperature gradient ∂Ts/∂z• Average temperature of snow pack, Tavg• Temperature-time variation dTs/dt• Ground temperature TgA system has been designed to measure above keytemperature parameters from which we can derive energyequations and hence other hydrological parameters. Thefollowing sections describe the design approach fordeveloping a Snow cover temperature profile measurementsystem.3. DESIGN OF SNOW TEMPERATUREMEASURING SYSTEM3.1 Physical DesignTo measure temperature distribution data, a Snow CoverTemperature Profile Measurement System has been designed.Proposed snow pack temperature profiler consists of a totalof 29 temperature sensors distributed in 3D fashion along a 4meter long PVC rod. This system measures accurately thetemperature of different layers of snow at multiple points atdifferent heights and different angles. Also sensor formeasuring ground temperature at different depths inside theground and true air temperature is a part of SnowTemperature Profile Sensor System (Shamshi et al., 1996).The system requires great design efforts within tightenvironmental and operational specifications. The probe hasto operate round the clock for several months undertemperature range from -50°C to +50°C with relativehumidity upto 100% and wind speed of the order of 200Km/h. The system was required to be accuracy and resolutionof 0.1°C. In view of these severe environmental conditions,the packaging has been designed water and moisture proof &wires and cables are to be selected so that these can withstandthese operational conditions. The components conform tomilitary specification standard JM5555/JM38510-883 (Attriet al., 2000a).3.1.1 Implementation of Snow Cover TemperatureProfile Sensors: Measurement of Tavg and ∂Ts/∂zOne-point measurement design can not be implemented herebecause of the very fact that different layers of snow packhave different properties, strength and energy contents andhence temperatures profile. We designed system architectureto support multi-point temperature measurements wheretemperature of all the points is to be measuredsimultaneously so as to minimize the effects of time drifts.Care of putting enough points of measurement in snow packhas been taken (Attri et al., 2000a). One most important pointis that points selected must be in three-dimensionalconfiguration.A mechanical design of spiral profiler system withpoints of measurement lying on an imaginary cylindricalsurface has been worked out. Refer to Fig. 2, in thisconfiguration, multiple platinum RTD temperature sensorswere spaced 30oapart in X-Z plane, 45oinclinationdownward of each of the mounted sensor in L-plane(cylindrical coordinates) and 20 cm apart in Y axis fromconsecutive sensors. Sensor sealed in metallic sheath ismounted on a triangular PVC assembly to give required slantof 45o. This slating angle made snow slide down & do notremain deposited over the probes during snow depletion. 30°horizontal spatial distances ensured that all directions aroundPVC mast are covered for temperature measurements. This
  • 4. R. Attri Instrumentation Design Series (Electronics), Paper No. 1, January 20004 | Copyright © 2000 Raman K. Attriarrangement gave overall 3-dimentional coverage of snow fortemperature measurements.Fig. 2: Angular and spatial Orientation of Sensors inCylindrical and Rectangular Planes. Each RTD sensor forsnow cover temperature distribution measurement ismounted at a spacing of 20cm from each other in H-plane,mounted at 30 deg angular spacing in R-plane from itsadjacent RTD sensors giving progressive spiral coverage asseen from ground interface upwards. Each of the RTDsensors is mounted 45 degree slated downwards to the Z-axis.Total 20 snow sensors have been used in theproposed snow Temperature Profile Sensor System to coverapproximately 4 meter of snowfall in a fashion shown in Fig.3. The graphical view of these 20 sensors as seen from top isshown in Fig. 4 with 30oseparation and its physicalimplementation is as seen in Fig. 5.Fig. 3: Enlarged View of a section of Snow Sensor PVCMast. Each RTS sensor is mounted at an angle of 45 degreewith the help of a PVC triangular block flushed to PVC tube,spaced 20cm from each other vertically.Fig. 4: Graphical representation of angular mountingarrangements of RTD sensors as seen from the top of thePVC mast. Each RTS sensor block is spaced 30 degrees in R-plane from its adjacent RTD. This provides 360 degreecoverage around the mast.
  • 5. R. Attri Instrumentation Design Series (Electronics), Paper No. 1, January 20005 | Copyright © 2000 Raman K. AttriThe leads from these sensors pass through the PVCtube and go to a junction box where analog unit of the systemis mounted. The junction box is mounted at such a heightthat it always remains out of snow cover. The analog outputis passed through low temperature cables to data logger (Attriet al., 2000a).Fig. 5: Physical mounting diagram depicting 30oSeparationbetween 10 adjacent Snow Sensors in Spiral Assembly fittedon 2-meter PCV tube block as seen in top view. Each 2-metersegment of PVC masts carries 10 RTD sensor blocks. Twosuch segments are used to mount 20 RTS sensor blocks.3.1.2 Implementation of Ground Temperaturesensors: Measurement of TgGround temperature is again important parameter to bemeasured. Here again layers of ground nearest to snowinterface have different temperature as compared to the coreground layers. Here 3D data is not important. So, here twodirectional measurements are enough. Logarithmic variationsof ground temperature have been taken into considerationand hence the mounting of ground temperature sensors hasbeen done accordingly. Total 7 number of ground sensors hasbeen mounted. 1 m of a PVC tube buried inside the groundis mounted with seven sensing probes with tips comingoutside at heights -5.0,-10.0,-20.0,-30.0,-50.0 and -100.0 cmrelative to ground.These7 ground sensors providestemperature profile of the ground and the temperaturegradient at ground interface. The Fig. 6 shows the groundsensors separations in –Z plane.The installation arrangement of 29 sensors has beenshown in Fig. 6. 20 snow sensors have been mounted on theremaining 4m of PVC mast outside the ground at thespacing of 20 cm each slanting downward at 45 degree angleand 30 deg apart in the horizontal plane from adjacentsensors.Fig. 6: Complete mounting arrangement and physicalarrangement of Snow Cover temperature profilemeasurement system. 20 RTD blocks mounted on twosegments of 2-meters each of PVC tube. 7 RTD sensorsmounted on PVC tube of 1 meter in length as buds touchingoutside the periphery. Ambient temperature stays outsidesnow cover. One IR surface sensor is mounted facingdownwards towards the snow surface.3.1.3 Implementation of Air temperature Sensor:Measurement of TairOne sensor is used to monitor the ambient temperature abovethe snow cover. This sensor is covered with a self-aspiratedradiation shield as shown in Fig. 7 so that sensor gives thetrue air temperature and is not affected by solar radiation.The air flows through the ventilation of this shield and raisesthe temperature of the sensing element. The heating causedby solar radiation and cooling caused by snowfall and raindoes not affect the reading of this temperature sensor. Onlythe true air temperature is read. This sensor is either to bemounted on the top of PVC tube or the supporting tower. Theambient temperature sensor has the flexibility of increasingor decreasing the height of sensor as the snow cover evolvesor depletes off.
  • 6. R. Attri Instrumentation Design Series (Electronics), Paper No. 1, January 20006 | Copyright © 2000 Raman K. AttriFig. 7: Mechanical Design of Radiation Shield for AmbientTemperature Sensor. The radiation shield is used to protectthe RTS sensor from direct solar radiations and to ensure itmeasures true ambient air temperature.3.1.4 Implementation of Snow surface TemperatureSensor: Measurement of TsSnow surface temperature is very difficult parameter tomeasure using any contact measurement method. Thethermal radiation emitted by Snow has been exploited in thedesign of Snow Surface Temperature Sensor. A separatesnow surface temperature sensor based on infrared techniquehas been designed as separate independent unit and has beenintegrated with the above system. The infrared radiationemitted by the optically radiative snow is collected by theproperly focused optical assembly. The temperature range ofthis sensor is from 0oC to –50oC with the resolution of 0.1oCin the measurement.Tight moisture proof system has been designed in asingle unit containing sophisticated optical assembly andassociated electronic circuit. Since the generated outputsignal is of very low level, signal conditioning unit isincorporated in single unit inside the compact module alongwith the optical assembly. The unit is installed at somesuitable height from the surface with the optically assemblyfacing vertically downward towards the snow. The system ispowered by the Data Collection Platform, which takes thereadings of the snow surface temperature after some fixinterval. The readings are stored in memory for furtherprocessing.3.2 Electronics DesignThe complete signal conditioning circuits of all the sensorsviz. snow sensors, ground sensors and air sensor arecontained in one single unit. This is a weatherproof sealedunit to with stand low temperature. The complete blockdiagram of the system is as shown in the fig 8Fig. 8: System Block diagram of Snow Temperature ProfileMeasurement System. The 4 sensor assembly namely 20 snowcover temperature RTD sensors, 7 ground temperature RTDsensors, 1 ambient sensor and 1 snow surface IR sensor. 28RTD sensors have a common signal conditioning unitwhereas IR sensor has its separate signal conditioning units.The output of signal conditioners is interfaced with a datalogger.The principle of resistance variations withtemperature has been used to measure Snow temperature.High accuracy, stable, precision metal film RTD sensoralong-with the associated circuitry has been used astemperature sensing element. These sensing elements areenclosed in metallic sheath filled with thermally conductiveAluminum Oxide. The compensation of self-heating, non-linearity and extension lead error in the sensor has beenprovided in the electronic design of the system (Attri et al.,200b). The accuracy of the order of one-tenth of a degreecentigrade is required with fair amount of linearity andstability.The temperature sensed at 29 different points in asnow pack plus air interface temperature from ambient sensoris stored in electronic data acquisition system. It is aprocessor-based unit with all facilities of modern highperformance data acquisition system. It controls the samplinginterval and multiplexing of 28 channels. The multiplexedsignal is given to A/D converter, which converts each analogvalue to the digital format. This digital data corresponds totemperature read by the corresponding sensor. This value issuitably computed by processor and converted intoengineering unit. The value is stored in memory locationsalong with sensor identification number and time ofrecording.The reading of temperature sensor is taken afterselectable timing interval. After every hour, all the samplesare computed to find out minima, maxima & averagetemperature of each sensor. The relative value in time givesthe required parameter of rate of change of temperature withtime ∂T/∂t. The computed data is important and is stored inseparate plug-in/plug-out memory modules. Provision ofdata retrieval from data logger through computer interface isalso given. Data is downloaded by computer and used forfurther processing and modeling of forecast. Data can be
  • 7. R. Attri Instrumentation Design Series (Electronics), Paper No. 1, January 20007 | Copyright © 2000 Raman K. Attriretrieved when required from these modules by reading themin memory reader in laboratory.Application software has been developed whichplots temperature vs height of sensor at different time. Thisgives air temperature, snow temperature profile as well asground temperature variations with time. This forms thebasis of energy exchange computation & hydrologicalinferences.The system is rigorously tested in the temperaturerange from –50oC to +50oC in the cold chamber.4. APPLICATION OF MEASURED DATA USINGSYSTEMThe Snow Cover temperature profile measurement systemhas been installed at Snow Avalanche Study Establishment(SASE) Manali in deep Himalayan regions (Shamshi et al.,1996). The Snow Temperature Profile Sensing systemincluding ground temperature sensors, ambient temperaturesensor and snow surface temperature sensor is used to get thehourly value of Average temperature of Snow, AverageTemperature of Air, Temperature gradient with respect toDepth of snow and temperature variation with respect to timeand average ground temperature.Ganju (1994) presented following method to usephysically monitored temperature data from the SnowTemperature Profile Sensor System to compute the energyexchange between air and snow pack and differenthydrological parameters which depends mainly upon thetemperature.• Energy used in cold content of top snow pack iscomputed• Energy that can be conducted through the snowpack is computed using one dimensional Fourierheat conduction equation with sources and sinks• The balance of energy is computed as subtraction ofenergy for cold content and energy conducted fromnet energy. Positive balance of energy used tocalculate the snowmelts.• The next reading of snow temperature is taken afteran hour. If snow temperature during next hour isobserved negative, net gain in energy is onceagain used to satisfy cold content, raise the layertemperature and compute melt, if any.• The Resultant snow layer thickness & density iscomputed on the basis of net melt.• Compute wetting front depth for dry snow pack.When the snow pack becomes isothermal, meltwater is percolated. Once the melt water reachesthe bottom of the snow pack, melt is taken out assub surface run-off.• Crust thickness is computed during the period ofnegative energy balance, as there is no melt.Using Armstrong approach, type of metamorphismand approximate size of grains are calculated. Using themodel of temperature profile, metamorphism and quantitiescomputed above, computer aided simulation model of snowcover formation, thickness, density, melt and strength isevolved which further is incorporated in snow avalancheforecast modeling, climatic forecast modeling and river runoff water determination modeling.5. CONCLUSIONData monitored by Snow temperature profile sensing systemhas been successfully working round the clock in Himalayanregion. The basic snow avalanche forecast model wadsdeveloped based on computer modelling of measuredtemperature data and using the equations of energy balance.However, mathematical models and equations used forextended computation and simulations are not solelydependent upon temperature parameters. The completeavalanche forecasting system requires range of other sensorsincluding snow depth sensor and humidity sensors. Acomprehensive forecasting system is developed bymonitoring snow depth and density, water contents and totalsnow covered area, morphological structure and crystalgrowth rate, temperature of warm rain and melt caused by it,reflectivity and absorption of solar radiation, porosity andstrength, wind speed etc.AcknowledgementsDr. M.A. Shamshi and Dr B>K. Sharma, Heads ofDepartment, Geo-Scientific Instruments Division, CentralScientific Instruments Organization to give an opportunity towork on this project.Mr V.P. Singh, Mrs Bupinder Kaur, Mr Rajender ShoundaTechnical officers, Geo-Scientific Instruments Division,Central Scientific Instruments Organization for theirtechnical support.REFERENCESAnderson EA (1976), A point energy and mass balance model of asnowcover, NASA technical reportAttri RK, Sharma BK, Shamshi MA (2000), Practical DesignConsiderations for Signal Conditioning Unit Interfaced withmulti-point Snow Temperature Recording System. IETETechnical Review, 17 (9): 351-61Attri, RK, Sharma BK, Shamshi MA, Sharma VP (2000) Design Approachto use Platinum RTD sensor in Snow TemperatureMeasurements, Journal of the Instrument Society of India, 30 (4): 275-283Bader HP and Wielenmann P (1992) Modelling temperature distribution,energy and mass flow in snowpack, Cold Region Science andtechnology, 20: 157-181Colbeck SC (1989), Snow crystal Growth with varying surface temperatureand radiation penetrations, Journal of Glaciology, 35 (119): 23-29Ganju A (1994) Snow cover model, Proceedings of SNOWSYPM-94, 221-226Hall DK (1985) Remote sensing of Ice and Snow, London: Chapman andHall PublicationsJordan R (1991) A one dimensional model for snow cover, CRREL SpecialreportMellor M (1977) Engineering properties of snow, Journal ofGlaciology, 19: 15-66
  • 8. R. Attri Instrumentation Design Series (Electronics), Paper No. 1, January 20008 | Copyright © 2000 Raman K. AttriOno, Wakatsuchi NM and Kawamura T (1976) Freezing phenomenon at seawater surface opening in polar winter, Low temperature Science39: 159-166Satyawali PK (1994) Grain Growth under temperature gradient, Proceedingsof SNOWSYPM-94, 5-8Schwerdtfeger P (1962) Theoretical derivation of Thermal conductivity anddiffusivity of snow, Int. Association of Scientific Hydrology,General Assembly of Berkley, BelgiumShamshi MA, Attri RK, SharmaVP (1996) Snow Pack Temperature sensor,Proceedings of National Conference on Sensors andTransducers, 180-189Singh AK (1994) Mathematical model for study of temperature profilewithin Snow cover. Proceedings of SNOWSYPM-94, 49-52Yamazaki, Kondo TJ, Sakuraoka T and Nakamura T (1993) A onedimensional model of evaluation of snow cover characteristics,Annual of Glaciology 18: 22-26.M.N.T. Graya and L.W. Morland (1994) A dry snow pack model, Journal ofCold Regions Science and Technology, Volume 22, Issue 2,January 1994, Pages 135-148Anderson, E.A. ( 1976). A point energy and mass balance model of a snowcover. NOAA Technical Report NWS 19, Office of Hydrology,National Weather Service, Silver Springs, MD.Jordan, R. (1996) A one-dimensional temperature model for a snow cover.Special report 657. US Army Cold Regions Research andEngineering Laboratory, Hanover, NH.C. H. Luce1 and D. G. Tarboton (2009) Evaluation of alternative formulaefor calculation of surface temperature in snowmelt models usingfrequency analysis of temperature observations, Hydrol. EarthSyst. Sci. Discuss., 6, 3863–3890, E. M. and Colbeck, S. C (1995).: Geometry of heat and mass transferin dry snow: a review of theory and experiment, Rev. Geophys.,33, 463–493.Bartelt, P. and Lehning, M (2002): A physical SNOWPACK model for theSwiss avalanche warning, 15 Part I: numerical model, ColdRegions Science and Technology, 35, 123–145.Jordan, R. (1991): A one-dimensional temperature model for a snow cover,Technical documentation for SNTHERM.89, US Army CRREL,Hanover, N.H. Special Technical Report 91-16, 49 pp.Koivasulo, H. and Heikinheimo, M (1999).: Surface energy exchange over aboreal snowpack: Comparison of two snow energy balancemodels, Hydrol. Process., 13, 2395–2408.Tarboton, D. G (1994): Measurement and Modeling of Snow EnergyBalance and Sublimation, International Snow ScienceWorkshopProceedings, Snowbird, Utah, 260–279,Tarboton, D. G., Chowdhury, T. G., and Jackson, T. H (1995): A SpatiallyDistributed Energy Balance Snowmelt Model, Biogeochemistryof Seasonally Snow-Covered Catchments, Boulder, Colorado,141–155.Brun, E., E. Martin, V. Simon, C. Gendre, and C. Coleou, (1989) An energyand mass model of snow cover suitable for operational avalancheforecasting. J. Glaciol., 35, 333–342.Bristow, K. L. and G. S. Campbell (1984) On the Relationship BetweenIncoming Solar Radiation and the Daily Maximum and MinimumTemperature. Agricultural and Forest Meteorology, 31: 159-166.Colbeck, S. C. and E. A. Anderson (1982) The Permeability of a MeltingSnow Cover. Water Resources Research, 18(4): 904-908.Gray, D. M. and D. H. Male, (Ed.) 1981. Handbook of Snow, Principles,processes,management & use. Pergamon Press: 776 pp.Koivasulo, H. and M. Heikenkeimo (1999) Surface energy exchange over aboreal snowpack. Hydrological processes, 13(14/15): 2395-2408.Luce, C. H. and D. G. Tarboton (2001) A modified force-restore approach tomodeling snow-surface heat fluxes. Proceedings of The 69thAnnual Meeting of the Western Snow Conference, Sun Valley,Idaho., D. G., T. G. Chowdhury and T. H. Jackson, (1995) A SpatiallyDistributed Energy Balance Snowmelt Model. In K. A.Tonnessen, M. W. Williams and M. Tranter (Ed.), Proceedings ofa Boulder Symposium, July 3-14, IAHS Publ. no. 228, pp. 141-155.Yen, Y. C. (1967). The rate of temperature propagation in moist porousmediums with particular reference to snow. Journal ofGeophysical Research, 72 (4): 1283-1288.Author Details:Author is Global Learning and Training Consultantspecializing in the area of performance technology. Hisresearch and technical experience spans over 16 yearsof project management, product development andscientific research at leading MNC corporations. Heholds MBA in Operations Management, ExecutiveMBA, Master degree in Technology and Bachelordegree in Technology with specialization in Electronicsand Communication Engineering. He has earnednumerous international certification awards - CertifiedManagement Consultant (MSI USA/ MRA USA),Certified Six Sigma Black Belt (ER USA), CertifiedQuality Director (ACI USA), Certified EngineeringManager (SME USA), Certified Project Director (IAPPM USA), to name a few. Inaddition to this, he has 60+ educational qualifications, credentials andcertifications in his name. His interests are in scientific product development,technical training, management consulting and performance technology.E-mail: rkattri@rediffmail.comWebsite: InformationWorking paper Copyrights © 2000 Raman K. Attri. Paper can becited with appropriate references and credits to author. Copying andreproduction without permission is not allowed.