From ILMS-Wiki

(Difference between revisions)

Revision as of 09:28, 19 October 2012

This tutorial describes the important processes and algorithm of the different modules within the J2000 hydrological model in detail:

Precipitation distribution module

Calibration parameters

parameter	description	Global range	For Dudh Kosi model
Trans	threshold temperature	0 + 5	2
Trs	base temperature for snow and rain	-5 +5	0

In the J2000 modelling system, the precipitation is first distributed between rain and snow depending upon the air temperature. Two calibration parameters (Trans, and Trs) are used where Trs is base temperature and Trans is a temperature range (upper and lower boundary) above and below the base temperature. In order to determine the amount snow and rain, it is assumed that precipitation below a certain threshold temperatures results in total snow precipitation and exceeding a second threshold results in total rainfall as precipitation. In the range (Trans) between those threshold temperatures, mixed precipitation occurs. Between those thresholds, rain-snow mixtures with variable percentages for each component are calculated. The acutal amount of snow (P(s)) of daily precipitation subject to air temperature is calculated according to:

$Ps = \frac{TRS + Trans - T}{2 \cdot Trans} \, \, \, \mathrm{[mm]}$

The daily amount of snow (P_s) or amount of rain (P_r) is calcualted according to:

$Ps = Precipitation \cdot Ps \,\,\, \mathrm{[mm]}$

$Pr = Precipitation \cdot (1- Ps) \,\,\, \mathrm{[mm]}$

These parameters are considered as non-flexible parameters and not necessarily placed in the JAMS framework as tunable parameters.

Relevancies in modelling

Putting the Trs values below zero (e.g. 2) will bring more precipitation in the form of 'rain' than 'snow'.

Interception module

Interception is a process during which the precipitation is stored in leaves, and other open surfaces of vegetation. During precipitation, interception by crop canopy and residue layer occurs. This process is identified as important components of a hydrological cycle that can affect the water balance components. Canopy and residue interception are considered losses to the system, as any rainfall intercepted by either of these components will subsequently be evaporated (Kozak et al. 2007). The interception module in the J2000 modelling system serves the calculation of the net precipitation from the observed precipitation against the particular vegetation covers and its development in the annual cycle. The observed precipitation is reduced by the interception part to calculate the net precipitation. Thus net precipitation only occurs when the maximum interception storage capacity of the vegetation is reached. The surplus is then passed on as throughfall precipitation to the next module. The interception module uses a simple storage approach according to Dickinson (1984), which calculates a maximum interception storage capacity based on the Leaf Area Index (LAI) of the particular type of land cover. The emptying of the interception storage is done exclusively by evapotranspiration. The maximum interception capacity (Int_max) is calculated according to the following formula:

$Int_{max} = \alpha \cdot{LAI} \, \, \, \mathrm{[mm]}$

with

α ... storage capacity per m² leaf area against the precipitation type [mm]

LAI ... LAI of the particular land-use class provided in land-use parameter file [-]

The parameter a has a different value, depending on the type of the intercepted precipitation (rain or snow), because the maximum interception capacity of snow is noticeably higher than of liquid precipitation. The LAI for individual vegetation types is provided in the land-use parameter file throughout the year. Because the LAI changes according to the seasons, four different LAI types for four different seasons for each vegetation type are proposed in land-use parameter file. The value of LAI can be determined by direct measurement of leaves, literature, and expert knowledge.

Snow module

Calibration parameters

parameter	description	Global range	For Dudh Kosi model
snowCritDens	Critical density of snow	0 to 1	0.381
snowColdContent	cold content of snowpack	0 to 1	0.0012
baseTemp	threshold temperature for snowmelt	-5 to 5	0
t_factor	melt factor by sensible heat	0 to 5	2.84
r_factor	melt factor by liquid precipitation	0 to 5	0.21
g_factor	melt factor by soil heat flow	0 to 5	3.73

These parameter are provided in bold and italic letters in the description below:

The snow module calculates the different phases of snow accumulation, metamorphosis and snowmelt. The more complex module is adapted in the model from Knauf (1980). The snow module takes into account the changes of state of snow pack during its existence, especially changes of snow density due to melting and subsidence. This process is important because snow pack can store free water, like a sponge, until reaching a certain threshold density and only then a sudden discharge of water occurs. For the model different water capacities of the snow pack are considered: the actual snow water equivalent (SWE_dry) which corresponds to the amount of water which has actually frozen and the total snow water equivalent (SWE_total) which in addition considers liquid water stored in the snow pack. The subsidence of the snow pack, which results from the liquid water through the snowmelt to the surface or from precipitation as rainfall, is calculated according to the empirical subsidence (snow-compaction scheme) by Bertle (1966).

The snow pack and its conditions are described in the modell according to the following parameters: snow depth (SD)[mm], dry snow density (dryDens)} [in g/cm³] as the quotient from total water content and snow depth.

If there is minimum, mean or maximum air temperature for a certain time (daily data), the module calculates separate accumulation or melt temperatures. Accumulation and melting can occur within a time step. The accumulation and melt temperatures (T_acc and T_melt) can be calculated according to:

$T_{acc} = \frac{T_{min} + T_{avg}}{2} \,\,\,\,\,\,[^oC]$

$T_{melt} = \frac{T_{max} + T_{avg}}{2} \,\,\,\,\,\,[^oC]$

Accumulation phase:

The snow module simulates accumulation and compaction of the snow pack caused by snowmelt or rain on snow precipitation.

The thermal circumstances under the snow cover are taken into account with the cold content in the snow cover in connection with the snowmelt. At the temperature below the freezing point, the snow pack cools down significantly. Because melted water freezes immediately due to negative isothermal circumstances under the snow cover, no runoff occurs. The cold content needs to reach the value zero so that the process of snowmelt begins again. Consequently, negative temperatures raise the cold content whereas the positive temperature reduces it. The calculation of storage of cold content results from the product of air temperature by a calibration parameter (coldContFact).

$CC = coldContFact \cdot T \,\,\,\,\,\,[mm]$

In doing so, negative air temperatures are accumulated and decreased only by positive temperature and resulting potential rates of melting. Only when the cold content has reached a value of 0, snowmelt occurs.

If the air temperature is below -15 C, the density of the new snow is assumed to be 0.02875.

The change of snow depth (δ SD) resulting from snow precipitation is calculated according to : Snow accumulation occurs in the model if precipitation falls in solid form (newSnow > 0). Therefore the density of new snow is determined subject to air temperature. The calculation is carried out according to (Kuchment 1983, and Vehvilaeinen 1992), if the air temperature is higher than -15 oC.

$newSnowDens = 0.13 + 0.0135 \cdot T_{acc} + 0.000045 \cdot T^{2}_{acc}\,\,\,\, [g/cm^3]$

If the air temperature is below -15 oC, the density of the new snow is assumed to be 0.02875.

The change of snow depth (δ SD) resulting from snow precipitation is calculated according to :

$δ SD = \frac{netSnow}{newSnowDens} \,\,\,\,\,\,[mm]$

The snow water equivalent of the previous day (\textit{SWEdry}) increases by the value of snow precipitation according to:

$SWEdry_{{t}} = SWEdry_{{t-1}} + netSnow \,\,\,\,\,\,[mm]$

The dry snow water equivalent and the total snow water equivalent are increased by the same value. If the precipitation event involved mixed (rain/snow) precipitation, the rain amount is allocated to the total snow water equivalent.

If rain is part of the precipitation event, it results in subsidence of the snow pack. The calculation of the subsidence amount is discussed below. In the model, the snow pack remains in the accumulation phase until the temperature value (T_melt) for the snowmelt exceeds a threshold value (baseTemp)which has to be determined during the parameterisation phase of the modeling application. Then it enters the metamorphosis phase which simulates melting and subsidence processes. However, it can go back to the accumulation phase if temperatures are correspondingly low. Due to different temperature values, accumulation and melting processes can be modeled during one time step.

Melting and subsidence phase:

If the melt temperature value (T_melt) exceeds the temperature limit value (baseTemp), the snow pack goes from the accumulation phase to the metamorphosis. The amount of energy which is required for snowmelt is available in three different ways. First, by input of sensible heat by air temperature (t_factor), second, by energy input from precipitation as rain (r_factor) and third, by input due to soil heat flow (g_factor). The sum of all energy inputs gives the potential snowmelt rate (Mp). The calculation of Mp is carried out according to:

$Mp = t\_factor \cdot T_{melt} + r\_{factor} \cdot netRain \cdot T_{melt} + g\_{factor} \,\,\,\,\,\,[mm]$

The variable Mp is then also modified according to the slope and the exposition of the spatial model entity (i.e. HRU):

$Mp = \ Mp \cdot actSlAsCf \,\,\,\,\,\,[mm]$

Mp is initially used to balance out the cold content of the snow cover and is then also used to generate snowmelt. The potential snowmelt rate then is taken to calculate the resulting maximum change of snow depth (δ SD):

$δ SD = \frac{M_P}{dryDens} \,\,\,\,\,\,[mm]$

If δ SD is greater than the entire snow depth, it defrosts completely and the entire snow water equivalent contributes to runoff generation in the form of snowmelt. If this is not the case, the snow depth is reduced correspondingly, which does not change the snow water equivalent at first. Rather the result is an increase in the total density of the snow cover.

In addition to this change in density, additional changes in subsidence and density according to the snow compaction-scheme (Bertle 1966) are taken into account. This method is based on the fact that water, no matter whether it results from temperature-induced snowmelt or from precipitation, seeps into the snow pack which leads to subsidence by recrystallization of snow and by structural changes and concentration in the storage (Knauf 1980). The resulting subsidence rate is calculated using the snow-subsidence method described in Bertle (1966). This method is based on the observation of an empirical relation between inflowing free water and the resulting change in elevation by subsidence which was derived from laboratory experiments of the US Bureau of Reclamation. For the calculation the increase of accumulated water content in percentage is seen in relation to the snow water equivalent using this formula:

$P_w = \frac{totSWE}{drySWE} \cdot 100 \,\,\,[\%]$

This equation shows that the more liquid water there is as input, the greater is the snow pack subsidence (P\_w) (Knauf 1980). An input of the exact the amount of water corresponding to the snow water equivalent of the snow pack leads to halving the snow depth by subsidence. The percentage of snow depth change (P$_H$) is calculated subject to the input of free water:

$P_H = 147.4 - 0.474 \cdot P_W \,\,\,[\%]$

The new snow depth (SD) is:

$SD = SD \cdot \frac{P_H}{100} \,\,\,[mm]$

Together with the snow depth which has been calculated the total density \textit{(totDens)} and the dry snow density \textit{(dryDens)} are calculated according to the following formulas:

$dryDens = \frac{SWE_{dry}}{SH} \,\,\,[g/cm^3]$

$totDens = \frac{SWE_{tot}}{SH} \,\,\,[g/cm^3]$

Melt runoff

The snow pack can store liquid water in its pores up to a certain critical density (snowCritDens). This storage capacity is lost nearly completely and irreversibly when a certain amount of liquid water in relation to the total SWE (between 40 and 45 percent) is reached according to Bertle (1966), Herrmann (1976) and Lang (2005). In this threshold limit, the retention capacity of a naturally developing snow pack is also suddenly decreased without rain impact. In such a case, a sudden water release from the snow pack can be observed (Herrmann 1976). In the model, this process is simulated by using the calculation of a maximum water content of the snow pack (SWE_max) according to :

$WS_{max} = snowCritDens \cdot SD \,\,\,\,\,\,[mm]$

The critical density (snowCritDens) needs to be provided by the model user. The water stored in the snow pack which exceeds this limit is conveyed as snow runoff (Q_snow).

$Q_{snow} = SWE_{tot} - SWE_{max} \,\,\,\,\,\,[mm]$

In the following time steps, the density of the snow pack keeps the critical threshold density until it is either defrosted or starts the accumulation due to recurring snowfall.

Glacier module

The glacier is developed and adapted as a part of the PhD research (Nepal, 2012) carried out in the Dudh Kosi river basin. The information provided here is taken from this study.

The glacier area is provided as a GIS layer which provides a unique land-use ID for glaciers during HRU delineation. All the processes which occur in the glacier are separately treated based on the unique ID. First the seasonal snow occurs on top of the glacier (or glacier HRU). The model first treats the snow as described in the 'Snow Module" and produces snowmelt runoff. In order to make sure that ice melt occurs, two conditions have to be met. First, the entire snow cover of a glacier HRU has to be melted (i.e.storage is zero), and second, the base temperature (tbase) as defined by users, has to be less than meltTemp. Only under these circumstances, the ice melt occurs as a model progress.

$meltTemp = \frac {Tmax + Tmean} {2} \,\,\,\,\,\,[^oC]$

The melt rate for glacier ice (iceMelt) (mm/day) is obtained by the following equation:

$iceMelt = \frac{1}{n} \cdot meltFactorIce + alphaIce \cdot radiation \cdot (meltTemp - tbase) \,\,\,\,\,\,[mm]$

where:

radiation = actual global radiation

meltFactIce = generalized melt factor for ice as a calibration parameter

alphaIce = melt coefficient for ice

n = time step (i.e. for daily model, n=1)

The ice melt is further adapted by the debris covered factor. Because the glaciers in the Dudh Kosi river basin are in general debris cover, a simple segregation method is applied to identify debris-covered glaciers based on slope. If the slope is higher than 30 degrees, the gravels, stones and pebbles are rolled down and the glacier is regarded as a clean glacier. The slope lower than this threshold is suitable for the accumulation of debris on top of glaciers. By using this approach, about 77 percent of the glaciers are estimated as debris-covered glaciers. According to Mool (2001a), about 70 percent of the glaciers in the Dudh Kosi river basin are valley types. One of the most common characteristics of glaciers located in the Himalayan region is the presence of debris material. In general, valley glaciers are debris-covered in the Himalayan region (Fujji 1977; Sakai2000}. It can be assumed that the debris-covered glacier areas estimated by this approach are fairly representative and adequate for purposes of this modelling application.

The presence of debris affects the ablation process. Supra-glacial debris cover, with thickness exceeding a few centimeters, leads to considerable reduction in melt rates (Oestrem 1959; and Mattson 1993). According to (Oestrem 1959) the melt rate decreased when the thickness of the debris cover was more than about 0.5 cm thick. The report further mentioned that not only the melting will be slower under the moraine cover, but also the ablation period will be shorter for the covered ice. The clean glaciers as reported on the Tibetan Plateau have higher retreat rates. (Kayastha 2000) studied the ice-melt pattern in the Khumbu glaciers (Dudh Kosi river basin where the J2000 model is being applied) and found that the debris ranging thickness from 0 to 5 cm indicates that ice ablation is enhanced by a maximum at 0.3 cm. Therefore, when a glacier is covered by debris, the ice melt is reduced. Using the calibration parameter (debrisFactor), the effects of debris cover on melt is controlled as follows.

$iceMelt' = icemelt - \left(icemelt \cdot \frac{debrisFactor}{10}\right)$

The icemelt is further adapted with the slope and aspect of the particular glacier HRU. Routing of glacier melt is made separately for snowmelt, ice melt and rain runoff using the following formula:

$Snow_{runoff} = meltRes_{t-1} \cdot e^ -\left(\frac {1}{kSnow}\right) \cdot Snow_{melt} \cdot e^ -\left(\frac {1}{kSnow}\right)$

where:

snow_melt = total snowmelt during the time step (mm/day)

meltRes_t-1 = outflow of reservoir during the last time step

kSnow = storage coefficient (recession constant) for reservoir

A similar routing procedure is applied for ice melt and rain runoff with a different recession constant (kIce) and (kRain). It is assumed that the routing of rain runoff is faster than that of ice and snow.

In reality, snow is stored in the accumulation zone of high-altitude areas. The snow is transported to low-altitude by wind, avalanches and gravity. As snow gets buried under new snow, it is gradually converted into firn and eventually into glacier ice. This ice flows by gravity downstream towards the ablation zone as glaciers (Jansson 2003). However, such dynamic processes of snow transformation and transportation are not included in the glacier module of the J2000 model. Therefore, some part of the precipitation is always stored as snow in the accumulation zone of high-altitude areas. To compensate for this long-term storage process, a constant glacier layer is used as a surrogate which provides melting from glacier ice.

Soil water module

The description of the soil water module as described in model source code is provided here which is primarily based on the technical documentation of the J2000 model (Krause, 2011).

In the soil module separate soils are represented according to their pore volumes. The pore storage which can occur in the soil are classified in the literature as follows (e.g. (Scheffer & Schachtschabel 1984)):

The water stored in fine pores (< 0.2 μm diameter, pF > 4.2, corresponds to the permanent wilting point - PWP) is so strongly bound due to its adsorption powers that it is not at all available for runoff generation.

The water stored in middle pores (diameter 0.2 to 50 μm, pF 1.8 to 4.2, corresponds to usable field capacity -nFk) is hold against gravity due to its adsorption powers. It can be extracted from the soil almost exclusively by using suction potential.

The water stored in coarse and macro pores (> 50 μm diameter, pF > 1.8, corresponds to air capacity - Lk) is subject to gravitation and can be kept in the soil for only a short period of time (1 to 2 days according to (Scheffer & Schachtschabel 1984, 1984).

Reach routing module

xx

@@ Line 236: / Line 236: @@
 In reality, snow is stored in the accumulation zone of high-altitude areas. The snow is transported to low-altitude by wind, avalanches and gravity. As snow gets buried under new snow, it is gradually converted into firn and eventually into glacier ice. This ice flows by gravity downstream towards the ablation zone as glaciers (Jansson 2003). However, such dynamic processes of snow transformation and transportation are not included in the glacier module of the J2000 model. Therefore, some part of the precipitation is always stored as snow in the accumulation zone of  high-altitude areas. To compensate for this long-term storage process, a constant glacier layer is used as a surrogate which provides melting from glacier ice.
-= Soil module =
+= Soil water module =
+The description of the soil water module as described in model source code is provided here which is primarily based on the technical documentation of the J2000 model (Krause, 2011).
+In the soil module separate soils are represented according to their pore volumes. The pore storage which can occur in the soil are classified in the literature as follows (e.g. (Scheffer & Schachtschabel 1984)):
+* The water stored in fine pores (< 0.2 μm diameter, pF > 4.2, corresponds to the permanent wilting point - PWP) is so strongly bound due to its adsorption powers that it is not at all available for runoff generation.
+* The water stored in middle pores (diameter 0.2 to 50 μm, pF 1.8 to 4.2, corresponds to usable field capacity -nFk) is hold against gravity due to its adsorption powers. It can be extracted from the soil almost exclusively by using suction potential.
+* The water stored in coarse and macro pores (> 50 μm diameter, pF > 1.8, corresponds to air capacity - Lk) is subject to gravitation and can be kept in the soil for only a short period of time (1 to 2 days according to (Scheffer & Schachtschabel 1984, 1984).
 = Reach routing module =
 xx

J2000 modules in detail

Revision as of 09:28, 19 October 2012

Contents

Precipitation distribution module

Interception module

Snow module

Glacier module

Soil water module

Reach routing module

Views

Personal tools

Navigation

Search

Toolbox