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HYPE can simulate tracers in addition to water flows, nutrients and organic carbon. Tracers are simulated as a substance given in info.txt and follow the water as a concentration. Two tracers are implemented;
T1 is the substance name for a general tracer. It can be used to simulate different substances, e.g. patogens or O18 isotope. The tracer is simulated as a concentration in HYPE's water bodies, e.g. snow, soil water, surface water. In addition T1 can be simulated as adsorbed to soil, as a store above ground, and in river sediments.
The following table shows how the unit of different tracers relates to each other and how they are related to input and output parameters and variables. The general unit (U) is used in tables of parameters and input data where the substance is not defined.
|Variabel/parameter||General unit (U)||Weight (kg)||Number of patogens (#)|
|Amount in manure/residuals (t1amount)||U/ha||kg/ha||#/ha|
|Point source concentration (ps_t1)||mU/m3 or µU/L||mg/L||thousandth part/m3 or millionth part/L|
|Concentration of water as incoming source (cpt1, t1leaksoil/t1leakluse)||mU/m3 or µU/L||mg/L||thousandth part/m3 or millionth part/L|
|Initial concentration parameters (init1, init1sw)||mU/m3 or µU/L||mg/L||thousandth part/m3 or millionth part/L|
|Simulated amount T1 in or above soil (aT11, aT12, aT13, sT11, sT12, sT13, T1sf)||U/km2||kg/km2||#/km2|
|Simulated amount T1 in river sediment (Tsmr, Tslr)||U||kg||#|
|Simulated concentration of water (coT1, ceT1, csT1, ccT1, clT1, Tcr1, Tcr2, Tcr3, Tcrd, Tcrs)||mU/m3 or µU/L||mg/L||thousandth part/m3 or millionth part/L|
|Observed concentration (reT1)||mU/m3 or µU/L||mg/L||thousandth part/m3 or millionth part/L|
There are four different ways to introduce the tracer T1 to the model:
1) T1 may be added as a concentration in precipitation (cpt1). This concentration is added as a time series in Xobs.txt.
2) Point sources may be a source of T1 to surface waters. Point sources of tracer T1 can be added to the local stream, the local lake, the main river or the outlet lake.
3) A pool laid down on land can be a source of the tracer. The pool is defined similar to the manure for nutrients (t1amount). It can be added at a specific point in time or equally distributed over a period of time. The pool may be tilled down into the top soil layers also in similar fashion as manure.
4) The tracer can be introduced to HYPE in the form of typical concentrations for leakage from different land-uses and/or soil types. The concentration of the runoff from a class (conc) is calculated as the product of two model parameters:
One parameter is land use dependent (t1leakluse) and one is soil type dependent (t1leaksoil).
The source of tracer by a typical concentration (introduction way 4) is not compatible with the sources concentration of precipitation (introduction way 1) and pool on the ground (introduction way 3).
In its basic state, T1 act as a tracer passively following the water through the model (except for evaporation). By supplying input data and parameter values this behaviour may be changed to simulate a non-conservative substance, e.g., a patogen.
As default T1 do not follow evaporating water. This is an exception from the basic assumption that T1 is a conservative tracer if no parameters are set. The tracer will follow evaporating water (with same concentration as the water it is evaporating from) if the model parameter t1evap is set to one. Default is zero. It is possible to set a value between zero and one so that the tracer partly follows evaporating water.
T1 can be released from a storage above ground (e.g. manure) by rain and snowmelt (flow q (mm/day)). The released tracer will follow the flow, as a concentration, and depending on the fate of the flow, the tracer may follow surface runoff, infiltration or other path ways. The release is goverened by the model parameter t1rel (1/mm). A fraction () of the total amount of tracer in the store above ground is released and follows the flow according to equation:
Patogens grow and die over time. To simulate this, HYPE supplies a process for the combined effect as an exponential decay. The process is goverened by the model paramater t1expdec, which denote the halv life time of the tracer in days. Exponential decay is applied to tracer T1 in most forms; in soil water, river, lakes, the above ground storage, tracers adsorbed to soil and tracers in river sediment.
Tracer adsorption/desorption to/from soil particles is calculated based on an equilibrium concentration ( (e.g. number of patogens/L or U/L)) of soil water. The equilibrium concentration is assumed to be reached within one time step of the model, typically one day, and this gives the amount of tracer adsorbed or desorbed during the time step is calculated. The equilibrium concentration () is calculated from the amount of tracers and soil characteristics. The equation is:
where Atot is the sum of tracer adsorbed and solved in soil water of the soil layer (U/km2), v the volume of water in the soil layer (mm), is soil density (kg soil/m3), and d is the thickness of the soil layer (m). The general model parameter t1freuc is an equlibrium concentration coefficient. In the case of patogens, the model parameter describes the number of patogens adsorbed to one kg of soil per patogens in one litre of soil water (or in general unit (U/kg soil)/(U/L) ).
Sedimentation or resuspension of tracers in rivers is calculated the same way as particulate phosphorus (described here). The process depends on the current flow (q) in the river in relation to bankful flow () and the general model parameter t1sedexp. Bankful flow is the flow when the river is filled to the brim. This flow is calculated as the second largest simulated flow in the last year. The fraction of the tracer that is resuspended or sedimented is determined by the equation:
For low flow, the fraction () is positive and sedimentation ( (U/day)) occur, for high flow the fraction is negative and there will be resuspension from the sediments instead ( (U/day)):
where is the concentration of T1 in river (U/m3), is the volume of river (m3), and Ased is amount of tracer T1 in the sediment (U).
Sedimentation of tracer T1 in lakes is calculated the same way as e.g. particular phosphorus. The sedimentation is goverend by sink velocity (m/d), which is given by the general model parameter t1sedvel.
Water temperature can be simulated by HYPE with the substance/tracer called T2. Water temperature is suitable to be simulated in a catchment model, because it relates to the hydrology and the landscape. The substance follows the water paths in HYPE and is calculated in degree Celsius.
There are different ways to introduce heat into the water of HYPE.
Initial value of water temperature of HYPE's water bodies can be set by model parameters. The general parameter iniT2 is used for some water bodies, i.e. soil, rivers and lakes. Aquifer temperature is given in AquiferData.txt.
Snow and glacier melt water is assumed to hold zero degrees.
Temperature of precipitation on land is set to air temperature (but limited to zero).
For water surfaces the temperature setting is more complex. Temperature of rain on water is set to air temperature (but limited to zero). Snowfall are assumed to have the average temperature of the water (uppertemp for lakes, mean temperature for rivers) for ice conditions, i.e. not to influence the temperature of the water. For snowfall on open water the temperature is calculated as dependent on sensible heat content and latent heat of freezing, taken into account different specific heat capacity of ice and water. Temperature of precipitation is a weighed average of these three components.
Point sources influence the water temperature T2. Point sources may have a constant temperature set from indata or otherwise the water is assumed to be zero degrees. Point sources of tracer T2 can be added to the local or main river, or internal or outlet lake.
The water of local diffuse source is not allowed to influence the water temperature of the recieving water body (soil or local river).
The primary process for changing water temperature is exchange of heat over a water surface. Apart from that, surface water temperature is determined by mixing water of different temperature. Exceptions have been made for some processes not to influence the water temperature. This because their effect on water temperature has not yet been included in full.
In addition to the “concentration” of T2 in soil water, the (solid) soil layer has their own temperature state variables. Temperatute of soil, i.e. solid material, is calculated separately from the T2 temperature of soil water. The temperature of a soil layer depends on the air temperature and the deep soil layer temperature to different degree. Deep soil layer temperature is calculated separately. See Chapter Soil temperature and snow depth.
Temperature T2 of soil water is not yet developed and is simply set to the temperature of soil. Still, snow melt are assigned the temperature T2 zero. Evaporation of soil water is not affected by T2 or affecting soil water T2.
Soil runoff temperature is set from soil layer temperatures. Tile drainage temperature is set to the temperature of the soil layer it originates from. Surface runoff gets the temperature from soil layer one (saturated overland flow) or rainfall, snowmelt and glaciermelt (excess infiltration).
Temperature T2 of a river is not affected by irrigation withdrawal, abstractions, rural households or point source additions, constructed wetlands, or water returning from aquifers.
For substances the lake volume is divided into two parts FLP and SLP (see Chapter Rivers and lakes - Basic assumptions)). In addition to simulating temperature as the substance T2 in the two lake parts, states of lake temperature in a hypothetical epilimnion and hypolimnion (uppertemp, lowertemp) is handled in the model. The average temperature of FLP+SLP is equal to the average temp of the EPI+HYPO. The size of volumes related to the upper and lower temperatures are determined by the thermocline which is estimated for each olake.
|Figure 2: Two different divisions of a lake. Left: two parts signifying fast flows (FLP) and slow flows (SLP). Right: epilimnion (EPI) and hypolimnion (HYPO).|
Thermocline depth is estimated from lake area (Hanna, 1990). This average depth is adjusted for current changes by adding precipitation (prec) and inflow (qin) to the lake, and remove evaporation (evap).
where lakearea is (km2) and epidepth is in m below lake surface. Precipitation, evaporation and inflow is also in meter.
The adjusted depth (epidepth) is then used as the division of the lake volume into upper and lower if the lake water depth is larger than the epidepth. Otherwise the lake is treated as one single mixed volume in regard to T2 calculations.
Rivers with area may have evaporation if they have an area.
The temperature T2 of the evaporating water is determined by the latent heat of vaporisation divided by the heat capacity. This temperature (heat) is then removed from the water with the evaporation. For calculation see Section Latent heat of vaporisation.
River evaporation is removed proportionally from the water stores making up the river volume. Lake evaporation may be removed from one or both lake parts (FLP and SLP). Evaporation from river or lake floodplain do not affect the T2. The water just evaporates keeping the temperature the same.
River and lake water atmosphere exchange is calculated during ice free conditions. Water surface heat balance is calculated based on a model by Piccolroaz et al (2013), with modifications for fractional ice cover, and calculation of fractional freezup area. This equation depends on four general parameters; tcf-temperature difference coefficient, scf - solar radiation coefficient, ccf - constant coefficient and lcf - linear coefficient. The parameters comes in one set for rivers (tcfriver, scfriver, ccfriver, lcfriver) and one set for lakes (tcflake, scflake, ccflake, lcflake).
Ice depth and snow depths are calculated for the freezed up fraction of the river or lake area. If the temperature is above freezing the excess heat is used to melt some ice from below.
At spring and autumn circulation, T2 temperature is averaged out between upper and lowertemp. During periods with stratification a heat transfer between the uppertemp and lowertemp is assumed.
Lake outflow T2 temperature may be determined by the T2 of the lake parts (FLP and SLP) contributing to outflow (see Figure 2). To use this method set parameter t2mix. For ilakes the t2mix method is always used.
For outlet lakes another method for determining lake outflow temperature is the default method. This method assigns uppertemp to outflow water if the lake is stratified and the thermocline is deeper than the lake threshold (thres). For other conditions a mixture of upper and lowertemp is used to set the outflow temperature (t2out).
where lakewst is the current depth of the lake.
Hanna 1990. Evaluation of models predicting mixing depth, Can. J. Fish. Aquat. Sci., 47:940-947.
Piccolroaz, S., M. Toffolon, and B. Majone 2013. A simple lumped model to convert air temperature into surface water temperature in lakes, Hydrol. Earth Syst. Sci., 17:3323-3338, doi:10.5194/hess-17-3323-2013.
|tracer_processes (t_proc.f90)||add_tracer_point_source_to_river||point source|
|calculate_lake_epilimnion_depth||lake basic assumptions|
|T2_processes_in_river||water - atmosphere T2 exchange|
|soilmodel_default (soilmodel0.f90)||soilmodel_0||soil temperature and runoff|