Meteorologi

Nr 122, 2006

Titel på framsidan i tjugotvå punkter och vänsterställd

Patrick Samuelsson, Stefan Gollvik, Anders Ullerstig Rossby Centre

The land-surface scheme of the Rossby Centre regional atmospheric climate model (RCA3)

Meteorologi

Nr 122, 2006Meteorologi

Nr 122, 2006

The land-surface scheme of the Rossby Centre regional atmospheric climate model (RCA3)

Patrick Samuelsson, Stefan Gollvik, Anders Ullerstig Rossby Centre

Report Summary / Rapportsammanfattning Issuing Agency/Utgivare

Swedish Meteorological and Hydrological Institute Report number/Publikation

Meteorologi nr 122 S-601 76 NORRKÖPING Sweden

Report date/Utgivningsdatum

December 2006 Author (s)/Författare

Patrick Samuelsson, Stefan Gollvik and Anders Ullerstig Title (and Subtitle/Titel

The land-surface scheme of the Rossby Centre regional atmospheric climate model (RCA3) Abstract/Sammandrag

This report describes the physical processes as part of the Land-Surface Scheme (LSS) in the Rossby Centre Regional Atmospheric Climate Model (RCA3). The LSS is a tiled scheme with the three main tiles with respect to temperature: forest, open land, and snow. The open land tile is divided into a vegetated and a bare soil part for latent heat flux calculations. The individual fluxes of heat and momentum from these tiles are weighted in order to obtain grid-averaged values at the lowest atmospheric model level according to the fractional areas of the tiles. The forest tile is internally divided into three sub-tiles: forest canopy, forest floor soil, and snow on forest floor. All together this gives three to five different surface energy balances depending on if snow is present or not.

The soil is divided into five layers with respect to temperature, with a no-flux boundary condition at three meters depth, and into two layers with respect to soil moisture, with a maximum depth of just above 2.2 meters. Runoff generated at the bottom of the deep soil layer may be used as input to a routing scheme.

In addition to the soil moisture storages there are six more water storages in the LSS: interception of water on open land vegetation and on forest canopy, snow water equivalent of open land and forest snow, and liquid water content in both snow storages.

Diagnostic variables of temperature and humidity at 2m and wind at 10m are calculated individually for each tile.

Key words/sök-, nyckelord

Land-Surface Scheme, Regional climate model Supplementary notes/Tillägg

Number of pages/Antal sidor

25

Language/Språk

English ISSN and title/ISSN och title

0283-7730 SMHI Meteorologi Report available from/Rapporten kan köpas från:

SMHI SE-601 76 NORRKÖPING Sweden

Contents

1 Introduction 2

2 General LSS setup 2

3 Specific LSS processes 4

3.1 Heat fluxes and aerodynamic resistance . . . . . . . . . . . . . . . . . . . . . . . . 5

3.2 Interception of rain on vegetation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

3.3 Surface resistances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

3.4 Evapotranspiration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3.5 Forest processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3.6 Open land and bare soil processes . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.7 Snow processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.7.1 Estimation of fractional snow cover . . . . . . . . . . . . . . . . . . . . . . 12

3.7.2 Snow temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3.7.3 Phase changes in snow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.8 Soil processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.8.1 Soil temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.8.2 Soil moisture, drainage and runoff . . . . . . . . . . . . . . . . . . . . . . . 16

A Aerodynamic resistances within the forest 18

B Snow density and snow albedo 19

B.1 Snow density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

B.2 Snow albedo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

C Diagnostic quantities 20

D Numerical details 21

D.1 Solving for Tf ora and q f ora . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

D.2 Solving the heat conduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

1

1 Introduction

Coupled numerical simulations over several decades are needed in order to better understand presentand future climate variability. The term coupled refers to atmospheric, land surface and oceanicprocesses. For long simulations it is important that the energy and water cycles are in balance. If anycycle is out of balance some flux corrections must be applied. In the case of regional modelling, themodel used as boundary condition will also keep the simulation on track.

Questions that the results from climate simulations aim to answer vary in both space and time. Forexample, farmers may want to know if the diurnal temperature range will change during the springseason in a specific region or the hydro-power industry might want to know if the annual water supplyto their dams will change with time. Thus, the model systems should be able to resolve variousprocesses on time scales ranging from hours to years.

Simulating variability on a short time scale (sub daily) involves fast-response processes. This meansthat complex feedback mechanisms involved must be more realistically described in the model thanis needed to capture only slower variability.

The aim of the present paper is to present a land-surface scheme (LSS) which has the ability to resolveprocesses ranging from hourly to annually. The LSS has been developed with focus on physicalprocesses which involve snow and frozen soil at mid and high latitudes. The main purposes of thescheme are: (i) to act as a lower boundary condition for the atmosphere. This means providing theatmosphere with realistic radiation, heat, and momentum fluxes, (ii) to provide the ocean with realisticrunoff and (iii) to realistically simulate some key land-surface diagnostics like 2 meter temperatureand humidity, 10 meter wind speed, and snow extent.

The LSS is part of the Rossby Centre Regional Atmospheric Climate Model (RCA3). For an evalua-tion of RCA3 please refer to Kjellstrom et al. (2006).

2 General LSS setup

The present scheme is a so-called tiled scheme which means that individual sub surfaces or tileswithin a grid square are characterised with unique values of surface properties like type of vegetation,roughness length and albedo. A separate energy balance is also calculated for each tile. Different tilesrespond differently to changes in fluxes depending on their heat capacity and heat transfer character-istics. Typical fast-response tiles are forest and snow surfaces. Forests have low heat capacity whilesnow has low heat transfer capacity. Thus, the temperature of these surfaces is quickly reflected in thegrid-averaged two meter temperature. Slower temperature changes depend largely on phase changesand the heat capacity of the whole soil column. In this case the amount of snow storage and soilfreezing processes are important.

Another approach in land surface modelling, which nowadays is being replaced by the tile approach,is the parameter averaging (mixture) approach. In the pure parameter averaging approach, all sub-surface properties of a grid square are averaged together so that only one value per grid square is usedfor each individual surface property. Here, only one energy balance is used to represent the wholegrid square. Generally the tile approach gives a better representation of the physical processes thanthe parameter averaging approach. However, for a very small scale, heterogeneous landscape and/orduring very windy conditions the parameter averaging approach will probably reflect the physicalprocesses more realistically (Koster and Suarez, 1992).

2

snTsn

Tam qam

wsn

wforc

rsvopl

woplvsnfor

rssopl

Tforsn

wforsn

Tforc

ToplsTfors

rssfor

rdrd

rsvfor+rb

rafor raoplrasn

Tforaqfora

zT1

zT2

zT3

zT4

zT5

z �1

z �2

AsnAoplAfor

Aforsn

Figure 1: A principal sketch of the land-surface scheme in RCA3. The LSS is divided into three maintiles: forest (A f or), open land (Aopl) and snow on open land (Asn). The forest also has a snow sub-tile(A f orsn). Prognostic temperatures are marked in red while the water prognostic variables are markedin blue. Each individual tile is connected to the lowest atmospheric level via their correspondingaerodynamic resistances (ra). For evapotranspiration calculations a number of surfaces resistancesare used (rs).

Parameter Definition ReferenceSub-grid fractionsA f or fractional area of forestAopl fractional area of open landAsn fractional area of open-land snow Sec 3.7.1A f orsn fractional area of snow in forest Sec 3.7.1Prognostic temperaturesTopls open land soil surface temperatureTsn snow surface temperature Eq 32Tsns soil temperature below snowTf orsn forest snow surface temperature Eq 24Tf ors forest soil surface temperature Eq 24Tf orsns soil temperature below forest snowTf orc forest canopy temperature Eq 24Prognostic water storagessn open land snow water equivalent Sec 3.7sn f or forest snow water equivalent Sec 3.7woplv intercepted water on low vegetation Sec 3.2w f orc intercepted water on forest canopy Sec 3.2wsn snow liquid water Sec 3.7w f orsn forest snow liquid water Sec 3.7

Parameter Definition ReferenceResistancesrsv f or forest canopy surface resistance Eq 10rsvopl open land vegetation surface resistance Eq 10rss f or forest floor soil surface resistance Eq 19rssopl open land soil surface resistance Eq 19ra f or aerodynamic resistance above forest Sec 3.1raopl aerodynamic resistance above open land Sec 3.1rasn aerodynamic resistance above snow Sec 3.1

rbaerodynamic resistance (forest canopy -canopy air)

Eq 46

rdaerodynamic resistance (forest floor -canopy air)

Eq 48

Depth of soil layers

zT 1–zT 5thickness of soil layers w.r.t. tempera-ture (0.01, 0.062, 0.21, 0.72, 1.89 m)

zθ1–zθ2

thickness of soil layers w.r.t. soil mois-ture (0.072, 2.2 m (1.0 m in mountain-ous areas))

Albedo and emissivity (value/prognostic)αopls open land surface albedo (0.28)α f orc forest canopy albedo (0.15)α f ors forest soil surface albedo (0.15)α f orsn forest snow surface albedo (0.2)αsn snow surface albedo (prognostic) Sec B.2εopls open land surface emissivity (0.985)ε f orc forest canopy emissivity (0.985)ε f ors forest soil surface emissivity (0.985)ε f orsn forest snow surface emissivity (0.99)εsn snow surface emissivity (0.99)εdesert desert surface emissivity (0.93)

3

From an atmospheric point of view, the present LSS, as shown in Figure 1, has three tiles with respectto temperature: forest, open land, and snow. The open land tile is divided into a vegetated and abare soil part for latent heat flux calculations. The individual fluxes of heat and momentum fromthese tiles are weighted in order to obtain grid-averaged values at the lowest atmospheric model levelaccording to the fractional areas of the tiles. Local surface layer equilibrium is assumed for each tilewhich means that they have their own aerodynamic resistances. The forest tile is internally dividedinto three sub-tiles: forest canopy, forest floor soil, and snow on forest floor. The motivation for thisdivision comes from the fact that these sub-tiles are closely related to each other with regards to theirtemperature and humidity conditions in the canopy air space. All together this gives three to fivedifferent surface energy balances depending on if snow is present or not.

The soil is divided into five layers with respect to temperature and consists of two to four sub-tilesdepending on if snow is present or not. The discretization of the soil generally follows that of Viterboand Beljaars (1995) except for the two top-most soil layers which are 1.0 and 6.2 cm, respectively. Atthe bottom we use a no-flux boundary condition.

There are eight prognostic water storages in the LSS: interception of water on open land vegetationand on forest canopy, snow water equivalent of open land and forest snow, liquid water content inboth snow storages, and two soil moisture storages. Interception of snow is not included.

The soil moisture is assumed to be independent on surface coverage which gives only two prognosticsoil moisture storages: top and deep soil moisture. The top soil moisture layer has a depth corre-sponding to the depth of the two top-most soil layers for temperature while the depth of the deep layeris 1.0 m in mountainous areas and 2.2 m outside mountainous areas. Runoff from the deep layer maybe used as input to a routing scheme.

Diagnostic variables of temperature and humidity at 2m and wind at 10m are calculated using Monin-Obukhov similarity theory as described in Appendix C. These diagnostic variables are calculatedindividually for each tile and are then area-averaged for larger sub-surfaces or for whole grid squares.

3 Specific LSS processes

Here, the individual processes as part of the LSS will be described separately. But, all these processesare tightly connected to each other. To illustrate this we take the 2m-temperature, representing one ofthe most important diagnostics produced by a LSS, as a starting point in the chain of dependenciesbetween the LSS processes. The 2m-temperature is a result of complicated feedback mechanisms be-tween the surface and the atmospheric surface layer. It is strongly connected to the prognostic surfacetemperatures which are closely related to the fluxes of sensible and latent heat. An underestimationof, for example, latent heat flux would produce a positive bias in sensible heat flux in order to fulfillthe energy balance, which implies a positive bias in the surface temperature. The problem is that therecould be many reasons for a wrong latent heat flux; the aerodynamic resistance could be wrong dueto incorrect roughness lengths or errors in the estimations of turbulence intensity, and in the case ofvegetation, errors in leaf area index (LAI), soil moisture content and surface resistance can all affectthe transpiration. The heat capacity of the surface elements (canopy, snow, soil surface) is importantfor the diurnal surface temperature variations which will affect surface saturation humidity and there-fore also the latent heat flux. These processes are certainly important for the diurnal variations in 2mtemperature but any errors will, of course, also affect the seasonal and annual mean temperatures.

To correctly describe seasonal and annual variations in 2m temperature, the LSS must also include

4

processes related to snow cover and soil freezing. Snow is an extreme in many respects. It has highalbedo which reduces available net radiation. It stores frozen water at the surface which requires alot of energy to melt, and it has low heat transfer capability which more or less isolates the soil fromthe atmosphere. Thus, it is very important to catch the areal and temporal extent of snow, not onlyfor simulating temperature, but also for river flows affected by snow melt. Soil freezing needs to beaccounted for since it acts to delay temperature drop in autumn and temperature rise in spring.

3.1 Heat fluxes and aerodynamic resistance

The sensible (H) and latent (E) heat fluxes between the surface and the first atmospheric level atheight zam (∼90 m in the present RCA3 set-up with 24 vertical levels) are parameterized as

H = ρcpTs −Tam

ra(1)

and

E = ρLeqs(Ts)−qam

ra + rs. (2)

Here, ρ is air density, cp is heat capacity of the air, Le is latent heat of vaporisation of water, Ts issurface temperature, Tam is temperature at zam, qs is surface saturated specific humidity, qam is specifichumidity at zam and ra aerodynamic resistance. The formulation of the surface resistance rs dependson the surface as described in Section 3.3.

The aerodynamic resistance is important for both fast response processes such as diurnal temperaturerange and for long term performance such as a correct division of precipitation into evapotranspirationand runoff. The LSS has three different aerodynamic resistances represented by the characteristics offorest, open land, and snow, with respect to surface temperature and roughness lengths of momentumand heat. The aerodynamic resistance for heat is given by the drag coefficient, Ch:

Ch =1

ura=

k2

ln(zam/z0m) ln(zam/z0h)fh(Ri,zam/z0h), (3)

where u is wind speed at zam, k is the von Karman’s constant, z0m and z0h are roughness lengthsfor momentum and heat, respectively, Ri is the Bulk-Richardson number and fh represents analyticstability functions based on modified Louis et al. (1981) formulations.

The dependence of the heat fluxes on the aerodynamic resistance is strong. This in turn has beenshown to be quite sensitive to the ratio between the roughness length of heat and momentum (Beljaarsand Viterbo, 1994; Chen et al., 1997; Samuelsson et al., 2003; van den Hurk and Viterbo, 2003).However, the problem is that estimations of the ratio z0m/z0h vary considerably. According to Chenet al. (1997) it is reasonable to relate the ratio to the properties of the flow as suggested by Zilitinkevich(1995):

z0m

z0h= exp(kC

√Re∗), (4)

where

5

Re∗ =u∗0z0m

ν, (5)

where ν is the kinematic molecular viscosity, Re∗ is the roughness Reynolds number, and u∗0 is thesurface friction velocity. C is an empirical constant which Chen et al. (1997) estimated to be 0.1based on comparisons between simulations and observations of heat fluxes. ra is sensitive to thevalue of C for large values on z0m (> 0.2 m) and to the value of z0m for small values on z0m (< 0.1m). The presently relatively thick (90 m) lowest atmospheric layer in RCA allows a long time stepof 30 minutes, but to maintain a reasonably high surface heat flux we have been forced to assumez0h = z0m = 0.2 m for snow free open land. Thus the Zilitinkevich formulation of the ratio z0m/z0h

is used only for snow surfaces with z0m = 0.002 m. For forest we use z0h = z0m as suggested byMolder and Lindroth (1999), which also gives good results when comparing simulated and observedheat fluxes. z0m for forest is a seasonally dependent value in the range 0.81–1.06 m.

3.2 Interception of rain on vegetation

Rain intercepted by the vegetation is available for potential evaporation which means that it has astrong influence on the fluxes of heat and consequently also on the surface temperature. So far inter-ception of snow is not included in the present LSS. A version exists where it is implemented and itwill be part the official LSS after further testing. Thus, at present we have only a prognostic storageof liquid water on the vegetation. Below freezing (T f orc ≤ 0◦C) rain is intercepted. Any water presentwill stay on the vegetation and evaporate as super-cooled water. The parameterization of interceptionof rain follows Noilhan and Planton (1989) and its implementation into RCA3 is similar to the imple-mentation in RCA2 as described by Bringfelt et al. (2001). The rate of change of intercepted water isdescribed by

wτ+1veg −wτ

veg

∆t= veg(P− δ

LeEv), (6)

where wveg is amount of intercepted water (mm of water on the specified fraction), τ and τ + 1 rep-resent present and next time step, ∆t is the length of the time step (s), veg is a vegetation coverparameter, P is rain intensity (kg m−2 s−1), Ev is evaporation of intercepted water (W m−2), and δ isthe fraction of of the vegetation covered with water defined as (Deardorff, 1978)

δ =

(

wveg

wvegmax

)2/3

. (7)

The exponent 2/3 comes from the fact that the intercepted water exists in the form of droplets wherethe water volume of the droplets is proportional to r3, where r is the radius of the droplets, and thesurface of the droplets is proportional to r2. wvegmax = 0.2 ·veg ·LAI is the maximum amount of waterallowed on the vegetation (Dickinson, 1984). Here LAI is the leaf area index as defined in Section3.3.

The evaporation Ev is calculated according to

Ev = ρLeqs(Ts)−qam

ra. (8)

6

To keep the solution numerically stable δ is solved implicitly

δ = (1−α)

(

wτveg

wvegmax

)2/3

+α

(

wτ+1veg

wvegmax

)2/3

, (9)

where α represents the degree of implicitly (set to 0.5). wτ+1veg is found by replacing δ in Equation 6

with Equation 9. The resulting equation is solved using the Newton-Raphson’s method.

The new value of intercepted water amount may not exceed the maximum value. Thus, any excesswater becomes throughfall, thr = max(0.0,(wτ+1

veg −wvegmax)/∆t). The final water amount is correctedwith the throughfall as wτ+1

veg = wτ+1veg − thr ·∆t and the total amount of rain that falls to the ground

becomes Ptot = thr +(1.0−veg)P.

This parameterization is used for interception of rain on both forest canopy and on open land vegeta-tion with individual values for the parameters veg and LAI. In the forest case Ts = Tf orc, qam = q f ora,and ra = rb and in the open land case Ts = Topls and ra = raopl .

3.3 Surface resistances

For latent heat flux a surface resistance is added for vegetation transpiration and for bare soil evapo-ration. Snow surfaces and intercepted water have zero surface resistance. In the case of condensation,qs(Ts) < qam, the surface resistance is also put to zero.

The vegetation surface resistance, closely following Noilhan and Planton (1989), is a function of avegetation dependent minimum surface resistance, rsvmin, the LAI, and five factors representing (F1)the influence of photosynthetically active radiation, (F2) the effect of water stress, (F3) the effect ofvapor pressure deficit, (F4) an air temperature dependence, and (F5) a soil temperature dependence:

rsv =rsvmin

LAIF1F−1

2 F−13 F−1

4 F−15 . (10)

The photosynthetically active radiation is assumed to be 0.55S↓, where S↓ is the incoming shortwaveradiation. The factor F1 is defined as

F1 =1+ f

f + rsvmin/rsvmax, (11)

with

f = 0.55S↓SL

2LAI

, (12)

where rsvmax is a maximum surface resistance set to 5000 s m−1 and SL is a limit value of 30 W m−2

for a forest and of 100 W m−2 for a crop.

The factor F2 varies between 0 and 1 depending on available soil moisture θ :

7

F2 =

1, if θ > θcrθ −θwi

θcr −θwi, if θwi ≤ θ ≤ θcr

0, if θ < θwi

(13)

where θwi is the wilting point, θcr = 0.9θ f c and θ f c is the field capacity. To account for differentsoil moisture conditions in different root layers the factor F2 is calculated individually for each soillayer which in combination with the other factors actually gives different rsv-values for each soil layer.These rsv-values are finally weighted with respect to the depth of each soil layer.

Factor F3 represents the effect of vapor pressure deficit of the atmosphere or, as expressed here, interms of specific humidity (Jarvis, 1976; Sellers et al., 1986):

F3 = 1−g(qs(Ts)−qam), (14)

where g is a vegetation-dependent empirical parameter set to 0.04 for a forest and to zero for a crop.In the forest case Ts = Tf orc and qam = q f ora and in the open land case Ts = Topls.

The air temperature has a strong influence on the transpiration with the most favorable conditions at25◦C. The factor F4 describes the air temperature dependence following Dickinson (1984)

F4 = 1.0−0.0016(298.0−Tam)2, (15)

where Tam = Tf ora in the forest case.

The vegetation does not become active in spring until the soil temperature in the root zone reachesat least +2◦C. Therefore, an additional factor, F5 = 1− f (T ), is added which varies between 0 and 1for soil temperatures between T1 = Tmelt + 4 K and T2 = Tmelt + 2 K following a sinusoidal functionoriginally intended for parameterization of soil freezing as described in Viterbo et al. (1999):

f (T ) =

0, T > T1

0.5

[

1− sin

(

π(T −0.5T1 −0.5T2)

T1 −T2

)]

, T2 ≤ T ≤ T1

1, T < T2.

(16)

As for F2, this gives different F5-values for different soil layers depending on their temperature.

There are separate leaf area indexes (LAI) for open land vegetation, for coniferous forest and for de-ciduous forest. The coniferous forest LAI, LAIc f , is set constant to 4.0 while the open land vegetationand deciduous forest LAIs are parameterised as functions of soil temperature (Hagemann et al., 1999):

LAIT = LAImin + f (Tsoil)(LAImax −LAImin), (17)

where

f (Tsoil) = 1−(

Tmax −Tsoil

Tmax −Tmin

)2

. (18)

8

The allowed range in LAI, defined by the maximum and minimum values LAImax and LAImin, are setto 0.4–2.3 for open land vegetation and to 0.4–4.0 for deciduous forest, respectively. LAI does notshow sub-diurnal variability. Thus, the soil temperature, Tsoil , in Equation 18 has to be unaffected bydiurnal variations why we have chosen the temperature in the fourth soil layer. The minimum andmaximum temperatures, Tmin and Tmax, are set to 273.0 and 293.0 K, respectively. All LAI values areset to LAImin for soil moisture values θs ≤ θwi, where θwi is the wilting point.

Bare soil evaporation is restricted by the soil surface resistance (van den Hurk et al., 2000):

rss =rssmin

1− f (T )

θ −θwi

θ f c −θwi, (19)

where rssmin represents a minimum value of the surface resistance (= 50 sm−1). As described inSection 3.8 there is no solid phase of soil water, therefore, 1− f (T ) is used to represent the fractionof liquid soil water to total soil water in the top soil layer with T1 = Tmelt +1 K and T2 = Tmelt −3 K.

3.4 Evapotranspiration

In the case of wet vegetation the total evapotranspiration is the sum of evaporation of interceptedwater, Ev in Equation 8, and transpiration via stomata, as expressed through Equation 2. The totalevapotranspiration, Ec, is defined as

Ec = ρLehvqs(Ts)−qam

ra + rsv, (20)

where the Halstead coefficient, hv, includes the fraction of the vegetation covered with water, δ ,

hv = htrv +hint

v = (1− kδ )+ra + rsv

rakδ . (21)

The coefficient is subdivided into a transpiration part, htrv , and into an interception part, hint

v . TheHalstead coefficient, as defined in Noilhan and Planton (1989), is modified by introducing the factork to take into account the fact that also saturated vegetation can transpire, i.e. when δ = 1 (Bringfeltet al., 2001). k=0 would represent a situation where the intercepted water forms full spheres justtouching the vegetation surface and therefore allow full transpiration from the whole leaf surface. k=1would represent a situation where a water film covers the vegetation completely and no transpirationis allowed. To adhere the interception model as described above, where the intercepted water existsas droplets, we set the value of k to 0.25. Note that in the case of condensation, i.e. Ec < 0, hv =(ra + rsv)/ra.

3.5 Forest processes

The forest canopy is characterized by low heat capacity which means that its temperature respondsfast to changes in fluxes. Thus, to realistically simulate diurnal variations in 2m-temperature in aforest dominated landscape this effect must be accounted for. The forest canopy acts more or less likea cover above the forest floor, therefore, it is really the temperature and specific humidity conditionsin the canopy air space, Tf ora and q f ora, that set the conditions for heat fluxes between forest canopy,

9

forest floor, and lowest model level in the forest tile. T f ora and q f ora are diagnostic variables whichhave to be solved iteratively as described in Appendix D. The heat fluxes are expressed as:

Sensible heat flux Latent heat flux

Forest canopy H f orc = ρcpTf orc −Tf ora

rbE f orc = ρLehv f or

qs(Tf orc)−q f ora

rb + rsv f or

Forest floor (soil) H f ors = ρcpTf ors −Tf ora

rdE f ors = ρLe

qs(Tf ors)−q f ora

rd + rss f or

Forest floor (snow) H f orsn = ρcpTf orsn −Tf ora

rdE f orsn = ρLe

qs(Tf orsn)−q f ora

rd

Canopy air - Atmos. H f or = ρcpTf ora −Tam

ra f orE f or = ρLe

qs(Tf ora)−qam

ra f or

(22)

Here rb and rd are the aerodynamic resistances between the forest canopy and the canopy air andbetween the forest floor and the canopy air, respectively. The Halstead coefficient, hv f or, is defined byreplacing ra with rb, rsv with rsv f or, and δ with δ f orc in Equation 21, respectively.

The bulk aerodynamic resistance rb and the aerodynamic resistance rd , defined in Appendix A, areboth based on Choudhury and Monteith (1988).

Since each sub surface within the forest tile has its own energy balance the net radiation componentsmust be separated between the forest canopy and the forest floor according to

Rn f orc = (1−χ)(1−α f orc)S↓ +(1−χ)ε f orc{L↓ +σ [(1−A f orsn)T 4f ors+

A f orsnT 4f orsn −2T 4

f orc]}Rn f ors = χ(1−α f ors)S↓ +ε f ors{χL↓ +σ [(1−χ)T 4

f orc −T 4f ors]}

Rn f orsn = χ(1−α f orsn)S↓ +ε f orsn{χL↓ +σ [(1−χ)T 4f orc −T 4

f orsn]}

(23)

where L↓ is incoming longwave radiation and α and ε are albedo and emissivity values, respectively,as specified in Figure 1. In the separation a sky view factor, χ = exp(−0.5 ·LAI), is used whichdescribes the degree of canopy closure and is defined as the fraction of sky that the ground under thecanopy sees (Verseghy et al., 1993). This definition is strictly valid only for longwave radiation incombination with needle-leaf trees. However, we apply it more generally, i.e., for all forest types andfor both short- and longwave radiation.

The total flux at the surface is defined as φ f orx = Rn f orx + H f orx + E f orx, where x is one of the sub-surfaces represented by forest canopy, forest soil, or forest snow. The total flux plus heat transferdetermine the time evolution of the surface temperatures

∂Tf orc

∂ t=

1C f orc

Φ f orc

∂Tf ors

∂ t=

1(ρC) f orszs

[Φ f ors +Λs(Tf ors2 −Tf ors)]

∂Tf orsn

∂ t=

1(ρC) f orsnz f orsn

[

Φ f orsn +Λ f orsn(Tf orsns −Tf orsn)]

(24)

where (ρC) f ors and (ρC) f orsn are volumetric heat capacities and Λs and Λ f orsn are heat transfer coeffi-cients as defined in Sections 3.8 and 3.7, respectively. The heat capacity of the forest canopy is defined

10

as C f orc = CvegWveg +Cwρww f orc, where Cveg is the vegetative heat capacity, Wveg is the standing massof the composite canopy, Cw is the specific heat of water, and w f orc is the amount of intercepted water(Verseghy et al., 1993). For the moment we assume the same vegetative heat capacity for all types oftrees.

3.6 Open land and bare soil processes

The open land tile, which includes low vegetation and bare soil, has its separate energy balancerepresented by the surface temperature Topls. The net radiation of the open land tile becomes Rnopls =(1−αopls)S↓ +εopls(L↓ +σT 4

opls) and the energy flux becomes

Hopls = ρcpTopls −Tam

raopl. (25)

The evapotranspiration from low vegetation is parameterized as

Eoplv = ρLehvoplqs(Topls)−qam

raopl + rsvopl, (26)

where hvopl is defined by replacing ra with raopl , rsv with rsvopl , and δ with δoplv in Equation 21,respectively.

The evaporation from bare soil is parameterized as

Eopls = ρLeqs(Topls)−qam

raopl + rssopl. (27)

3.7 Snow processes

A snow surface is very different from most other surfaces found over land. It is characterized by veryhigh albedo and the snow itself has low heat capacity and very limited heat transfer capability. It isimportant to realistically simulate the fractional coverage of snow since snow is related to at least twoimportant positive feedback loops. An overestimated fractional snow cover will lead to an overes-timated area averaged albedo. This will reduce the amount of absorbed short wave radiation at thesurface and cause a reduction in temperature which will be favourable for further snow accumulation.An underestimation of fractional snow cover during the spring will lead to an underestimated area av-eraged albedo which will tend to raise the temperature and accelerate the snow melt and a reduction insnow cover. Unfortunately snow cover is one of the most difficult snow related processes to simulate.

There are two separate snow packs in the present LSS: one on open land, where the fluxes directlycommunicate with the lowest model layer, and one in the forest, where the fluxes depend on thecanopy air temperature and humidity. Except for the albedo, which is prognostic for open-land snowbut constant for forest snow, the snow scheme is identical for the two snow packs.

11

3.7.1 Estimation of fractional snow cover

An open-land surface, initially with no snow cover, may be totally snow covered for only a smallamount of snowfall. This would imply a very thin snow layer. Since snow has a low heat capacitysuch a thin layer could cause very rapid temperature changes in a numerical scheme and consequentlynumerical instability. Thus, for numerical reasons the fractional snow cover must increase graduallywith increasing snow amount.

During the growing phase, the snow cover fraction, Asn, is parameterized to asymptotically approacha maximum allowed snow cover fraction, Asnlim set to 0.95, as a function of the snow water equivalentsn according to

Asn = Asnlim tanh(100sn), (28)

where the factor 100 is a constant controlling the rate of growth. Asnlim is set to less than one fornumerical reasons but also because a landscape mostly includes rough surfaces and obstacles thatalways tend to create snow free areas. For a snow layer not reaching Asnlim in coverage the sameformulation of snow cover is used during the melting phase.

If the snow pack has accumulated over a long enough time and reached over a certain limit in cover-age, set to Asnlim − 0.001, the snow cover fraction during the melting phase is described differently.According to observations the snow cover for deep snow packs is better correlated with the ratiosn/snmax than with sn itself, where snmax is the maximum snow water equivalent reached during thesnow season (Lindstrom and Gardelin, 1999). To simulate this process we store the memory of thesnow pack in snmax. When Asn = Asnlim −0.001 is reached snmax is put equal to sn and during the restof the snow season snmax is kept larger than or equal to sn. During this period the snow cover fractionis parameterised according to

Asn =sn

snmax∆sn f rd,Asn ≤ Asnlim, (29)

where ∆sn f rd is a snow fraction distribution factor. Thus, during snow melt Asn will be kept at Asnlim

until sn = snmax∆sn f rd is reached. According to observations of snow cover reported in Lindstrom andGardelin (1999) ∆sn f rd is a function of orography. In mountainous areas ∆sn f rd tend to be higher thanin less mountainous areas. Based on these observations the following formulation is used

∆sn f rd = 0.6+0.001σorog,∆sn f rd ≤ 0.8, (30)

where σorog is the degree of subgrid orography calculated as the standard deviation of the orographyfor a specific grid resolution based on the GTOPO30 database.

When the end of the snow season approaches, defined as when snτ+1 < k1snτmax, snmax is gradually

decreased to zero to allow for a new season to start following the function

snτ+1max = snτ

max − (k1snmax − snτ+1)(1− k)/k1, (31)

where k1 = 0.2 and k = exp(10−6∆t).

12

Temperature

Depth

0

zT1

zsn

Tsn Tsns

Thermally activesnow layer, zsn

*

a)

Temperature

Depth

0

zT1

zsn

Tsn Tsns

b)

zsn*

Figure 2: Principal sketch of the assumed temperature profile in a thin (a) and in a thick (b) snowlayer respectively.

3.7.2 Snow temperature

The purpose of the parameterization of snow in the present LSS is to give a reasonable surface tem-perature of the snow and a reasonable evolution of the snow pack including runoff of melt water. Acorrect surface temperature is especially important for the net long wave radiation on the diurnal timescale. On this time scale we assume that only the uppermost part of a thick snow layer is thermallyactive due to the limited heat transfer capability of snow. Thus, we use a bulk snow layer concept,only regarding the thermal properties of the snow in this layer. There will be a heat transfer also atthe snow-soil interface which must be parameterized. Phase changes in the snow between snow andwater are important to consider since such processes may have a strong influence on the temperatureevolution. To account for these processes any snow melt water is partly kept in the snow as liquidwater which can freeze again when the energy balance at the snow surface becomes negative.

Figure 2 shows the concept used describing the assumed temperature profile in the snow for a thinand for a deep snow layer, respectively. The depth of the thermally active layer is defined as z∗sn =min(zsn,zsnmax), where zsn is the actual snow depth and zsnmax = 0.15m is the maximum depth of thethermally active layer. The actual snow depth is defined as zsn = snρw/ρsn, where ρsn and ρw are thedensities of snow and water, respectively. ρsn is a prognostic variable in the present LSS as describedin Appendix B.

The equation for the snow temperature is as follows:

∂Tsn

∂ t=

1(ρC)snzsn

[Φsn +Λsn(Tsns −Tsn)] , (32)

where (ρC)sn = (ρC)iceρsn/ρice is the volumetric heat capacity of the snow and (ρC)ice is the vol-umetric heat capacity for ice. Φsn = Rnsn + Hsn + Esn is the sum of the energy fluxes at the snowsurface, net radiation and sensible and latent heat fluxes, respectively, defined as

Rnsn = (1−αsn)S↓ +εsn(L↓ −σT 4sn), (33)

Hsn = ρcpTsn −Tam

rasn, (34)

13

Esn = ρLeqs(Tsn)−qam

rasn. (35)

Note that these equations refer to the open land snow and must be replaced by the correspondingforest equations in the case of forest snow. The snow albedo, αsn, is defined in Appendix B.

The snow temperature in the layer below the thermally active layer is in principal unknown whichmeans that the heat transfer at the snow-soil interface is parameterised using a heat transfer coefficientΛsn between the snow and the underlying soil layer. Basically it is assumed that the heat transfer atthe snow-soil interface decreases with the depth of the snow layer. Λsn is simply a weighted averageof the heat transfer coefficients of snow and soil, respectively, defined as

Λ−1sn = 0.5

zsn

λsn+0.5

zT 1

λT, (36)

where λsn = λice(ρsn/ρice)1.88 and λT is defined in Equation 42 and λice = 2.2 W m−1 K−1.

The snow temperature equation is part of a heat conduction problem including the soil temperatureequations. The resulting equation system is solved implicitly. In the case of phase changes, i.e.melting of snow or freezing of liquid water in the snow, the time step is divided into two parts, onewhere the temperature of the snow is kept constant and one where the snow temperature is allowed tochange.

3.7.3 Phase changes in snow

Two types of phase changes can take place in the snow pack; at positive energy balance the snowtemperature increases until the melting temperature is reached and melting starts, while at negativeenergy balance any liquid water in the snow can partly refreeze at the same time as the snow tem-perature drops. One can use different strategies to numerically solve this phase-change problem. Wehave chosen to divide the time step into two parts which means that upon melting, one part of thetime step is used for increasing the temperature and the other part is used to melt snow while keepingthe snow temperature at the melting point. Upon freezing, one part of the time step is used to freezeliquid water while keeping the snow temperature constant and the other part is used to decrease thesnow temperature.

The total energy per unit time available for the snow is

Φtot = Φsn +Λsn(Tsns −Tsn). (37)

If Φtot > 0, we estimate the time, ∆tdtemp, it takes to bring Tsn to Tmelt using Equation 32. If ∆tdtemp ≥∆t the melting temperature is not reached and the snow temperature is calculated using Equation 32with ∆tdtemp = ∆t. If ∆tdtemp < ∆t Equation 32 is used to bring Tsn to Tmelt and then Φtot is usedduring the rest of the time step, ∆td phase = ∆t −∆tdtemp, to melt snow while Tsn is kept at the meltingtemperature. The amount of melted snow, or water, becomes

snmel =∆td phaseΦtot

ρwL, (38)

14

where L is the latent heat of freezing. This amount is used to increase the amount of liquid water keptin the snow, wsn, until it reaches a maximum allowed amount, wsnsat = ∆snsatsn, where ∆snsat is set to10%. Any excess liquid water goes to the soil.

At negative energy balance for the snow, i.e. Φtot < 0, the snow temperature should drop but if theliquid water content is non-zero we should also freeze some of the water. In contrast to the straightforward melting processes the parameterisation of the freezing process is not as obvious in the case ofwsn > 0. How much of the liquid water that should be frozen during a certain time does, in principle,depend on where the water is located in the snow layer and how the characteristics of the heat transferin the snow looks like. With a snow model as simple as the one described here it is impossible tomake any physically valid estimation on this amount. Thus, we are let out to some estimation basedon assumptions. The assumptions made here are based on the fact that snow melt mainly occurs at thetop of the snow layer and that the melt water is located where melting occurs. The larger the amountof melt water in the snow the deeper it penetrates. We estimate a fraction, ∆ f reeze, of the liquid wateramount that is allowed to freeze according to

∆ f reeze = min

(

sn f reezeρsn

ρw

∆snsat

wsn,1

)

, (39)

where sn f reeze is an assumed depth of snow over which freezing is allowed to be active, set to 0.03 m.In other words, the equivalent water amount corresponding to sn f reeze is sn f reezeρsn/ρw. The corre-sponding maximum liquid water amount allowed is given by sn f reezeρsn/ρw∆snsat which is related tothe actual liquid water amount, wsn. The value of sn f reeze must be estimated by trial and error exam-ining the simulated snow temperature against observations. ∆ f reeze is used to calculate the fraction ofthe time step to be used for freezing of water, ∆td phase = ∆ f reeze∆t. During this time the snow temper-ature is kept constant. Cooling of the snow temperature takes place during the rest of the time step,∆tdtemp = ∆t −∆td phase, by applying Equation 32. If the available water is less than the correspondingwater given by ∆td phase, the time for freezing of water is reduced.

The change in open-land snow water equivalent is as follows:

snτ+1 = snτ +∆tρw

[

Asn(F +Psn−)+Aopl(F +Popl−−Fopl+)+AsnEsn

Le

]

− snmel, (40)

which includes the three phase changes Psn−, rain freezing on cold snow, Popl−, rain freezing on coldground and Fopl+, snow melting on warm ground. F denotes snowfall (kg m−2s−1). The change inforest snow water equivalent is given by a corresponding equation.

3.8 Soil processes

The soil is characterized by its texture and water content. The present scheme uses seven differenttexture classes based on the geographical distribution of soil types FAO-Unesco (1981) digitized forEurope by the German Weather Service. These classes are sand, loam, clay, sandy loam, silt loam,sandy clay, and peat. The hydraulic properties for each soil type are based on Clapp and Hornberger(1978) and McCumber and Pielke (1981) and are specified in terms of total porosity θsat (m3m−3),field capacity θ f c (m3m−3), wilting point θwi (m3m−3), matric potential at saturation ψsat (m), hy-draulic conductivity at saturation γsat (m s−1), Clapp and Hornberger soil parameter b, and volumetricdry soil heat capacity (ρC)s (Jm−3K−1).

15

3.8.1 Soil temperature

The soil heat transfer equation applied for each soil layer can be written as

[(ρC)sθ +∆C f s]∂Ts

∂ t=

∂∂ z

(

φ t,b +λT∂Ts

∂ z

)

. (41)

Here (ρC)sθ is the volumetric wet soil heat capacity for a soil moisture content of θ (m3m−3) definedas (ρC)sw = (ρC)s +θρwCw.

The present LSS does not include the solid phase of soil water which means that e.g. the thermalprocess related to the latent heat of fusion/freezing is absent. This process is important since it actsto delay the soil cooling in autumn and the soil warming in spring. To simulate this effect we applya modification of the soil heat capacity, ∆C f s, as suggested by Viterbo et al. (1999), which increasesthe total soil heat capacity in the temperature range -3 to +1◦C.

The heat conductivity λT depends on the soil water content as described by McCumber and Pielke(1981)

λT (θ) = −aψ−1/ log10sat

(

θsat

θ

)−b/ log10

. (42)

Here a is an empirical soil thermal conductivity parameter.

The top boundary condition, φ t , is represented by the total flux at the surface, φ f ors or φopls in thecases of forest soil or open-land soil, respectively, or the heat transfer at the soil/snow interface in thecases of snow covered soil in the forest or at the open land as defined in Section 3.7. At the bottom azero-flux condition is assumed, i.e. φ b = 0.

Since there are four different top boundary conditions for the soil we will have four soil columns withdifferent evolutions of their soil temperature profiles. The soil is divided into five layers in the verticalwith respect to temperature which thus results in 20 prognostic soil temperatures. If the fractionalsnow cover changes during a time step the soil temperatures have to be adjusted accordingly to avoidan artificial change of the total heat content of the soil.

3.8.2 Soil moisture, drainage and runoff

The vertical transport of water in the unsaturated soil is usually expressed using Richards equation(Hillel, 1980)

∂θ∂ t

=∂∂ z

(

λ∂θ∂ z

)

− ∂γ∂ z

+S(θ ,z), (43)

where λ is the hydraulic diffusivity (m2s−1), γ is the hydraulic conductivity (ms−1), and S(θ ,z) isa volumetric source/sink term (m3m−3s−1). The hydraulic diffusivity is parameterized according toMcCumber and Pielke (1981)

λ =bγsat(−ψsat)

θsat

(

θθsat

)b+2

. (44)

16

The volumetric source/sink term generally includes effects of precipitation, runoff, root extraction,and phase changes of ice to liquid water. However, as described above we do not explicitly includeany phase changes of ice to liquid water in the soil but instead we parameterize the effect that soilice would have had on soil heat capacity and root extraction. In the present LSS we replace thehydraulic conductivity term, ∂γ/∂ z, in Equation 43 with a drainage/runoff parameterization as part ofthe S(θ ,z) term. The final sources and sinks in S(θ ,z) then become; supply of water at the soil surface,Sw(z0), evaporation/condensation at the soil surface, Se(θ ,z0), loss due to root extraction, Sre(θ ,zd),and drainage/runoff, Sdr(θ ,zd), at each soil layer/interface zd . No lateral transport of water existsin the scheme. The supply of water at the soil surface is represented by contributions from rainfall,snow-melt water, and throughfall from vegetation. The evaporation/condensation at the soil surface isrepresented by two terms; one for the forest floor soil, which is the E f ors equation in Equation array22, and one for the open land soil, Equation 27.

The loss due to root extraction is given by the transpiration parts of Equations 22(E f orc) and 26, i.e.with the transpiration components of the Halstead coefficients, htr

v f or and htrvopl .

The drainage/runoff parameterization is based on the so called β -formulation as used in the hydro-logical HBV model (Lindstrom et al., 1997). The drainage can then be written as a source/sink term

Sdr(θ ,zn) = Sdr(θ ,zn−1)

(

θ −θwi

θ f c −θwi

)β, (45)

where the upper boundary condition Sdr(θ ,z0) = Sw(z0) and the resulting runoff is given by Sdr(θ ,z2).The exponent β set to zero would imply a grid square with no water holding capacity at all while ahigh β value indicates such homogeneous conditions that the whole grid square may be regarded as abucket that overflows when its field capacity is reached. β is thus more an index of heterogeneity thanof soil property. β is a tuning parameter and in the present model we use the same value as is used inthe HBV model, which is 2 for both soil layers (Bergstrom and Graham, 1998).

17

A Aerodynamic resistances within the forest

The parameterisation of the bulk aerodynamic resistance rb = 1/gb is based on Choudhury and Mon-teith (1988), where the conductance between the canopy and the canopy air, gb, is defined as

gb =2LAIa

α ′

(u f or

lw

)1/2[1− exp(−α ′/2)]. (46)

The conductance is modified with a free convection correction according to Sellers et al. (1986)

gb = gb +LAI890

(

Tf orc −Tf ora

lw

)1/4

. (47)

The aerodynamic resistance rd is based on Choudhury and Monteith (1988)

rd =z f or exp(α)

αK(z f or)[exp(−αz′0/z f or)− exp(−α(d + z0)/z f or)], (48)

where

K(z f or) = k(z f or −d)u∗ f or =k2(z f or −d)u

lnz f or−d

z0

. (49)

The displacement height is defined as (Choudhury and Monteith, 1988):

d = 1.1z f or ln[1+(cdLAI f )1/4] (50)

where the leaf drag coefficient cd is defined as (Sellers et al., 1996):

cd = 1.328

[

2

Re1/2

]

+0.45

[

1π

(1−χL)

]1.6

(51)

where χL is the Ross-Goudriaan leaf angle distribution function, which has been estimated accordingto Monteith (1975) (see Table 1), and Re is the Reynolds number defined as

Re =ullw

υ. (52)

The unstable transfer correction for rd = rd/ψH according to Sellers et al. (1986), where

ψH =

[

1+9Tf ors −Tf ora

Tf orsu2f or

z f or

]1/2

. (53)

For the estimations of rb and rd the friction velocity at the forest tile, u∗ f or, is needed as well as thewind speed at the top of the forest, i.e. u f or at z f or. u∗ f or is estimated from the drag coefficient ofmomentum calculated as in Equation 3 but with z0h replaced by z0m. u f or is then reached in two steps:firstly the wind speed utrans at a transition level ztrans, located between zam and z f or, is calculated as

18

u(ztrans) =u∗ f or

k

[

lnztrans −d

z0m−Ψm

(

ztrans −dL

)]

, (54)

where ztrans is defined as

ztrans = z f or +11.785z0m. (55)

Secondly, u f or = u(ztrans)−G2∆u(ztrans,z f or), where ∆u(ztrans,z f or) = u(ztrans)− u(z f or) and G2 isan adjustment factor which is equal to 0.75 according to Xue et al. (1991).

Table 1: Surface independent parameters

Symbol Definition Unit Value Reference Comment

g Acceleration of gravity m s−2 9.81G2 Adjustment factor - 0.75 Xue et al. (1991) Eq. 13k von Karman constant - 0.4a m s−1/2 0.01 Choudhury and Monteith (1988) Eq. 26α ′ attenuation coeff. for wind - 3 Choudhury and Monteith (1988) p 386lw leaf width m 0.02α attenuation coeff. for mom. - 2 Choudhury and Monteith (1988) p 386z′0 roughness of soil surface m 0.007χL Ross-Goudriaan leaf angle dist. - 0.12 Monteith (1975) p 26ul Typical local wind speed m s−1 1 Sellers et al. (1996) Eq. B7υ Kinematic viscos. of air m2 s−1 0.15×10−4

B Snow density and snow albedo

B.1 Snow density

The density of the snow increases exponentially with time towards a maximum value as long as nofresh snow is added by snowfall. The total density of the snow pack is a weighted value of the drysnow and of the liquid water content. Assuming that we have the density of the dry snow calculated,ρsnd , which compare to the water equivalent of the dry snow, snd , we can combine that with anysnowfall, F , during the time step to a temporary new dry snow density

ρ∗snd =

snτdρτ

snd +(∆tF/ρw)ρsnmin

snτd +(∆tF/ρw)

, (56)

where ρsnmin = 100 kg m−3 is the minimum density of dry snow. The new value of the dry snowdensity becomes

ρτ+1snd = (ρ∗

snd −ρsnmax)exp(−τ f ∆t/τ1)+ρsnmax, (57)

where ρsnmax = 300 kg m−3 is the maximum density of dry snow. The time scales τ1 = 86400 s andτ f = 0.24 give an e-folding time of about 4 days. Combining the new dry snow density with the liquidwater content in the snow gives the total density of the snow

19

ρτ+1sn = ∆τ+1

snd ρτ+1snd +(1−∆τ+1

snd )ρw, (58)

where ∆snd is the fraction of dry snow to total snow, i.e. ∆snd = (sn−wsn)/sn.

B.2 Snow albedo

The net radiation balance at the surface for open land snow is given by Rnsn = (1−αsn)S↓ +εsn(L↓−σT 4

sn), where the snow albedo, αsn, for open-land snow is a prognostic variable. The albedo forsnow in the forest is put constant to 0.2. The parameterisation of snow albedo evolution with time isbased on Verseghy (1991) and Douville et al. (1995). For non-melting conditions the albedo decreaseslinearly with time according to

ατ+1sn = ατ

sn − τa∆t/τ1, (59)

where τa = 0.008, while for melting conditions the albedo decreases exponentially with time accord-ing to

ατ+1sn = [ατ

sn −αmin]exp(−τ f ∆t/τ1)+αmin, (60)

where αmin = 0.50. If the snowfall exceeds 1/3600 kg m−2 s−1 the snow albedo is set to ατ+1sn =

αmax = 0.85.

C Diagnostic quantities

Except for prognostic variables at the surface and at atmospheric model levels there is a need tocalculate diagnostic variables that correspond to common observed quantities. Some of the mostimportant diagnostic variables are air temperature and specific humidity at 2m height (T 2m and q2m)and wind speed components at 10m height (u10 and v10). The calculation of these diagnostic variablesfor a given height z are based on Monin-Obukhov similarity theory:

u(z) = u∗k

[

ln zz0m

−Ψm(

zL

)

]

v(z) = v∗k

[

ln zz0m

−Ψm(

zL

)

]

T (z) = Ts + θ∗k

[

ln zz0h

−Ψh(

zL

)

]

q(z) = qs + q∗k

[

ln zz0q

−Ψq(

zL

)

]

(61)

where u∗ and v∗ are friction velocities, θ∗ and q∗ are temperature and humidity scales, respectively, k isthe von Karman’s constant, z0m, z0h and z0q are roughness lengths for momentum, heat and humidity,respectively, L is the Monin-Obukhov length, Ts and qs are surface values, and Ψx represents analyticstability functions for momentum, heat and humidity, respectively.

In RCA3 these equations are approximated to (Woetmann Nielsen, 1987):

Stable case:

20

u(z) = u∗k ln z

z0m+uam

[

1− exp(

− 1kRicr

u∗uam

zL

)]

v(z) = v∗k ln z

z0m+ vam

[

1− exp(

− 1kRicr

v∗vam

zL

)]

T (z) = Ts + θ∗k ln z

z0h+(Tam −Ts)

[

1− exp(

− 1kRicr

θ∗Tam

zL

)]

q(z) = qs + q∗k ln z

z0q+(qam −qs)

[

1− exp(

− 1kRicr

q∗qam

zL

)]

(62)

where Ricr = 0.25, z0q = z0h and subindex am represents lowest atmospheric model level.

Unstable case:

u(z) = u∗k

[

ln zz0m

−(

ln 1+x2

2 +2ln 1+x2 −2tan−1 x+ π

2

)]

v(z) = v∗k

[

ln zz0m

−(

ln 1+x2

2 +2ln 1+x2 −2tan−1 x+ π

2

)]

T (z) = Ts + θ∗k

[

ln zz0h

−2ln 1+y2

]

q(z) = qs + q∗k

[

ln zz0q

−2ln 1+y2

]

(63)

where x = (1−15z/L)1/4 and y = (1−9z/L)1/2.

The Monin-Obukhov length is defined as

L = − u3∗T

kgw′θ ′v

=u3∗

kgHv/cp

ps −d phRd

=u3∗

kgHv/(ρcp)Tam (64)

where the buoyancy flux Hv is defined as

Hv = H +0.61cpTamE/Le. (65)

u10, v10, T 2m and q2m are all calculated separately for each tile. Any diagnostic values representinggroups of tiles or the whole grid square are calculated as area averaged values.

D Numerical details

D.1 Solving for Tf ora and q f ora

The heat fluxes in Equations 22 are functions of Tf ora or q f ora but so are also the aerodynamic resis-tances included in the equations. Thus, the equilibrium value of T f ora with respect to the temperaturesTf orc, Tf ors, Tf orsn, and Tam has to be solved for iteratively. Tf ora is solved from the relationship

H f or = H f orc +(1−A f orsn)H f ors +A f orsnH f orsn (66)

which gives

Tf ora =

Tamra f or

+(1−A f orsn)Tf ors+A f orsnTf orsn

rd+

Tf orcrb

1ra f or

+ 1rd

+ 1rb

. (67)

21

q f ora is solved for in a similar manner with a corresponding equation for latent heat fluxes as the onefor sensible heat fluxes in Equation 66.

D.2 Solving the heat conduction

Once the fluxes are computed we solve the heat conduction for each tile, using the implicit methodof Richtmeyer and Morton (1967). The degree of implicity is set to 0.5, except for the fast variables,Tf orc, Tf ors, Tf orsn and Topls, which are treated fully implicitly.

Acknowledgments:

The authors are grateful for discussions with Bjorn Bringfelt and with colleagues at Rossby Cen-tre, SMHI, who gave valuable input to this report. We would also like to acknowledge colleagueswithin the HIRLAM community and contacts with other researchers who have been helpful in thedevelopment of the present LSS.

22

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25

SMHIs publiceringar SMHI ger ut sex rapportserier. Tre av dessa, R-serierna är avsedda för internationell publik och skrivs därför oftast på engelska. I de övriga serierna används det svenska språket. Seriernas namn Publiceras sedan RMK (Rapport Meteorologi och Klimatologi) 1974 RH (Rapport Hydrologi) 1990 RO (Rapport Oceanografi) 1986 METEOROLOGI 1985 HYDROLOGI 1985 OCEANOGRAFI 1985 I serien METEOROLOGI har tidigare utgivits: 1985 1 Hagmarker, A. (1985)

Satellitmeteorologi. 2 Fredriksson, U., Persson, Ch., Laurin, S.

(1985) Helsingborgsluft.

3 Persson, Ch., Wern, L. (1985)

Spridnings- och depositionsberäkningar för av fallsförbränningsanläggningar i Sofielund och Högdalen.

4 Kindell, S. (1985)

Spridningsberäkningar för SUPRAs anläggningar i Köping.

5 Andersson, C., Kvick, T. (1985)

Vindmätningar på tre platser på Gotland. Utvärdering nr 1.

6 Kindell, S. (1985)

Spridningsberäkningar för Ericsson, Ingelstafabriken.

7 Fredriksson, U. (1985)

Spridningsberäkningar för olika plymlyft vid avfallsvärmeverket Sävenäs.

8 Fredriksson, U., Persson, Ch. (1985)

NOx- och NO2-beräkningar vid Vasaterminalen i Stockholm.

9 Wern, L. (1985)

Spridningsberäkningar för ASEA transformers i Ludvika.

10 Axelsson, G., Eklind, R. (1985) Ovädret på Östersjön 23 juli 1985.

11 Laurin, S., Bringfelt, B. (1985)

Spridningsmodell för kväveoxider i gatumiljö.

12 Persson, Ch., Wern, L. (1985)

Spridnings- och depositionsberäkningar för avfallsförbränningsanläggning i Sofielund.

13 Persson, Ch., Wern, L. (1985)

Spridnings- och depositionsberäkningar för avfallsförbränningsanläggning i Högdalen.

14 Vedin, H., Andersson, C. (1985)

Extrema köldperioder i Stockholm. 15 Krieg, R., Omstedt, G. (1985)

Spridningsberäkningar för Volvos planerade bilfabrik i Uddevalla.

16 Kindell, S. Wern, L. (1985)

Luftvårdsstudie avseende industrikombinatet i Nynäshamn (koncentrations- och luktberäkningar).

17 Laurin, S., Persson, Ch. (1985)

Beräknad formaldehydspridning och deposition från SWEDSPANs spånskivefabrik.

18 Persson, Ch., Wern, L. (1985)

Luftvårdsstudie avseende industri-kombinatet i Nynäshamn – depositions-beräkningar av koldamm.

19 Fredriksson, U. (1985) Luktberäkningar för Bofors Plast i

Ljungby, II.

20 Wern, L., Omstedt, G. (1985) Spridningsberäkningar för Volvos planerade bilfabrik i Uddevalla - energi-centralen.

21 Krieg, R., Omstedt, G. (1985)

Spridningsberäkningar för Volvos planerade bilfabrik i Uddevalla - kompletterande beräkningar för fabrikerna.

22 Karlsson, K.-G. (1985)

Information från Meteosat - forskningsrön och operationell tillämpning.

23 Fredriksson, U. (1985)

Spridningsberäkningar för AB Åkerlund & Rausings fabrik i Lund.

24 Färnlöf, S. (1985)

Radarmeteorologi. 25 Ahlström, B., Salomonsson, G. (1985)

Resultat av 5-dygnsprognos till ledning för isbrytarverksamhet vintern 1984-85.

26 Wern, L. (1985)

Avesta stadsmodell. 27 Hultberg, H. (1985)

Statistisk prognos av yttemperatur. 1986 1 Krieg, R., Johansson, L., Andersson, C.

(1986) Vindmätningar i höga master, kvartals-rapport 3/1985.

2 Olsson, L.-E., Kindell, S. (1986)

Air pollution impact assessment for the SABAH timber, pulp and paper complex.

3 Ivarsson, K.-I. (1986)

Resultat av byggväderprognoser - säsongen 1984/85.

4 Persson, Ch., Robertson, L. (1986)

Spridnings- och depositionsberäkningar för en sopförbränningsanläggning i Skövde.

5 Laurin, S. (1986)

Bilavgaser vid intagsplan - Eskilstuna.

6 Robertson, L. (1986) Koncentrations- och depositions-beräkningar för en sopförbrännings-

anläggning vid Ryaverken i Borås. 7 Laurin, S. (1986)

Luften i Avesta - föroreningsbidrag från trafiken.

8 Robertson, L., Ring, S. (1986)

Spridningsberäkningar för bromcyan. 9 Wern, L. (1986)

Extrema byvindar i Orrefors. 10 Robertson, L. (1986)

Koncentrations- och depositions- beräkningar för Halmstads avfalls- förbränningsanläggning vid Kristinehed. 11 Törnevik, H., Ugnell (1986)

Belastningsprognoser. 12 Joelsson, R. (1986)

Något om användningen av numeriska prognoser på SMHI (i princip rapporten

till ECMWF). 13 Krieg, R., Andersson, C. (1986)

Vindmätningar i höga master, kvartals- rapport 4/1985. 14 Dahlgren, L. (1986)

Solmätning vid SMHI. 15 Wern, L. (1986)

Spridningsberäkningar för ett kraftvärme-verk i Sundbyberg.

16 Kindell, S. (1986)

Spridningsberäkningar för Uddevallas fjärrvärmecentral i Hovhult.

17 Häggkvist, K., Persson, Ch., Robertson, L

(1986) Spridningsberäkningar rörande gasutsläpp från ett antal källor inom SSAB Luleå-verken.

18 Krieg, R., Wern, L. (1986)

En klimatstudie för Arlanda stad. 19 Vedin, H. (1986)

Extrem arealnederbörd i Sverige. 20 Wern, L. (1986)

Spridningsberäkningar för lösningsmedel i Tibro.

21 Krieg, R., Andersson, C. (1986)

Vindmätningar i höga master - kvartals-rapport 1/1986.

22 Kvick, T. (1986) Beräkning av vindenergitillgången på några platser i Halland och Bohuslän.

23 Krieg, R., Andersson, C. (1986)

Vindmätningar i höga master - kvartals-rapport 2/1986.

24 Persson, Ch. (SMHI), Rodhe, H.

(MISU), De Geer, L.-E. (FOA) (1986) Tjernobylolyckan - En meteorologisk analys av hur radioaktivitet spreds till Sverige.

25 Fredriksson, U. (1986)

Spridningsberäkningar för Spendrups bryggeri, Grängesberg. 26 Krieg, R. (1986)

Beräkningar av vindenergitillgången på några platser i Skåne.

27 Wern, L., Ring, S. (1986)

Spridningsberäkningar, SSAB. 28 Wern, L., Ring, S. (1986)

Spridningsberäkningar för ny ugn, SSAB II.

29 Wern, L. (1986)

Spridningsberäkningar för Volvo Hallsbergverken.

30 Fredriksson, U. (1986)

SO2-halter från Hammarbyverket kring ny arena vid Johanneshov.

31 Persson, Ch., Robertson, L., Häggkvist, K.

(1986) Spridningsberäkningar, SSAB - Luleå-verken.

32 Kindell, S., Ring, S. (1986)

Spridningsberäkningar för SAABs planerade bilfabrik i Malmö.

33 Wern, L. (1986)

Spridningsberäkningar för svavelsyrafabrik i Falun.

34 Wern, L., Ring, S. (1986)

Spridningsberäkningar för Västhamns-verket HKV1 i Helsingborg.

35 Persson, Ch., Wern, L. (1986) Beräkningar av svaveldepositionen i Stockholmsområdet.

36 Joelsson, R. (1986)

USAs månadsprognoser.

37 Vakant nr.

38 Krieg, R., Andersson, C. (1986) Utemiljön vid Kvarnberget, Lysekil.

39 Häggkvist, K. (1986)

Spridningsberäkningar av freon 22 från Ropstens värmepumpverk.

40 Fredriksson, U. (1986)

Vindklassificering av en plats på Hemsön.

41 Nilsson, S. (1986) Utvärdering av sommarens (1986) använda konvektionsprognoshjälpmedel.

42 Krieg, R., Kvick, T. (1986)

Vindmätningar i höga master. 43 Krieg, R., Fredriksson, U. (1986)

Vindarna över Sverige. 44 Robertson, L. (1986)

Spridningsberäkningar rörande gasutsläpp vid ScanDust i Landskrona - bestämning av cyanvätehalter.

45 Kvick, T., Krieg, R., Robertson, L. (1986)

Vindförhållandena i Sveriges kust- och havsband, rapport nr 2.

46 Fredriksson, U. (1986)

Spridningsberäkningar för en planerad panncentral vid Lindsdal utanför Kalmar.

47 Fredriksson, U. (1986)

Spridningsberäkningar för Volvo BMs fabrik i Landskrona.

48 Fredriksson, U. (1986)

Spridningsberäkningar för ELMO-CALFs fabrik i Svenljunga.

49 Häggkvist, K. (1986)

Spridningsberäkningar rörande gasutsläpp från syrgas- och bensenupplag inom SSAB Luleåverken.

50 Wern, L., Fredriksson, U., Ring, S. (1986)

Spridningsberäkningar för lösningsmedel i Tidaholm.

51 Wern, L. (1986) Spridningsberäkningar för Volvo BM ABs anläggning i Braås.

52 Ericson, K. (1986) Meteorological measurements performed May 15, 1984, to June, 1984, by the SMHI.

53 Wern, L., Fredriksson, U. (1986) Spridningsberäkning för Kockums Plåt-teknik, Ronneby.

54 Eriksson, B. (1986)

Frekvensanalys av timvisa temperatur-observationer.

55 Wern, L., Kindell, S. (1986)

Luktberäkningar för AB ELMO i Flen. 56 Robertson, L. (1986)

Spridningsberäkningar rörande utsläpp av NOx inom Fagersta kommun.

57 Kindell, S. (1987)

Luften i Nässjö. 58 Persson, Ch., Robertson, L. (1987)

Spridningsberäkningar rörande gasutsläpp vid ScanDust i Landskrona - bestämning av cyanväte.

59 Bringfelt, B. (1987)

Receptorbaserad partikelmodell för gatumiljömodell för en gata i Nyköping.

60 Robertson, L. (1987)

Spridningsberäkningar för Varbergs kommun. Bestämning av halter av SO2, CO, NOx samt några kolväten.

61 Vedin, H., Andersson, C. (1987)

E 66 - Linderödsåsen - klimatförhållanden. 62 Wern, L., Fredriksson, U. (1987)

Spridningsberäkningar för Kockums Plåtteknik, Ronneby. 2.

63 Taesler, R., Andersson, C., Wallentin, C.,

Krieg, R. (1987) Klimatkorrigering för energiförbrukningen i ett eluppvärmt villaområde.

64 Fredriksson, U. (1987)

Spridningsberäkningar för AB Åetå-Trycks planerade anläggning vid Kungens Kurva.

65 Melgarejo, J. (1987)

Mesoskalig modellering vid SMHI. 66 Häggkvist, K. (1987)

Vindlaster på kordahus vid Alviks Strand -numeriska beräkningar.

67 Persson, Ch. (1987)

Beräkning av lukt och föroreningshalter i luft runt Neste Polyester i Nol.

68 Fredriksson, U., Krieg, R. (1987) En överskalig klimatstudie för Tornby, Linköping.

69 Häggkvist, K. (1987)

En numerisk modell för beräkning av vertikal momentumtransport i områden med stora råhetselement. Tillämpning på ett energiskogsområde.

70 Lindström, Kjell (1987)

Weather and flying briefing aspects. 71 Häggkvist, K. (1987)

En numerisk modell för beräkning av vertikal momentumtransport i områden med stora råhetselement. En koefficient-bestämning.

72 Liljas, E. (1988)

Förbättrad väderinformation i jordbruket - behov och möjligheter (PROFARM).

73 Andersson, Tage (1988)

Isbildning på flygplan. 74 Andersson, Tage (1988)

Aeronautic wind shear and turbulence. A review for forecasts.

75 Kållberg, P. (1988)

Parameterisering av diabatiska processer i numeriska prognosmodeller.

76 Vedin, H., Eriksson, B. (1988) Extrem arealnederbörd i Sverige 1881 - 1988.

77 Eriksson, B., Carlsson, B., Dahlström, B.

(1989) Preliminär handledning för korrektion av nederbördsmängder.

78 Liljas, E. (1989)

Torv-väder. Behovsanalys med avseende på väderprognoser och produktion av bränsletorv.

79 Hagmarker, A. (1991)

Satellitmeteorologi. 80 Lövblad, G., Persson, Ch. (1991)

Background report on air pollution situation in the Baltic states - a prefeasibility study. IVL Publikation B 1038.

81 Alexandersson, H., Karlström, C.,

Larsson-McCann, S. (1991) Temperaturen och nederbörden i Sverige 1961-90. Referensnormaler.

82 Vedin, H., Alexandersson, H., Persson, M. (1991) Utnyttjande av persistens i temperatur och nederbörd för vårflödesprognoser.

83 Moberg, A. (1992)

Lufttemperaturen i Stockholm 1756 - 1990. Historik, inhomogeniteter och urbaniseringseffekt. Naturgeografiska Institutionen, Stockholms Universitet.

84 Josefsson, W. (1993)

Normalvärden för perioden 1961-90 av globalstrålning och solskenstid i Sverige.

85 Laurin, S., Alexandersson, H. (1994)

Några huvuddrag i det svenska temperatur-klimatet 1961 - 1990.

86 Fredriksson, U. och Ståhl, S. (1994)

En jämförelse mellan automatiska och manuella fältmätningar av temperatur och nederbörd.

87 Alexandersson, H., Eggertsson Karlström,

C. och Laurin S. (1997). Några huvuddrag i det svenska nederbördsklimatet 1961-1990.

88 Mattsson, J., Rummukainen, M. (1998)

Växthuseffekten och klimatet i Norden - en översikt.

89 Kindbom, K., Sjöberg, K., Munthe, J.,

Peterson, K. (IVL) Persson, C. Roos, E., Bergström, R. (SMHI). (1998) Nationell miljöövervakning av luft- och nederbördskemi 1996.

90 Foltescu, V.L., Häggmark, L (1998)

Jämförelse mellan observationer och fält med griddad klimatologisk information.

91 Hultgren, P., Dybbroe, A., Karlsson, K.-G.

(1999) SCANDIA – its accuracy in classifying LOW CLOUDS

92 Hyvarinen, O., Karlsson, K.-G., Dybbroe, A. (1999) Investigations of NOAA AVHRR/3 1.6 µm imagery for snow, cloud and sunglint discrimination (Nowcasting SAF)

93 Bennartz, R., Thoss, A., Dybbroe, A. and Michelson, D. B. (1999) Precipitation Analysis from AMSU (Nowcasting SAF)

94 Appelqvist, Peter och Anders Karlsson (1999) Nationell emissionsdatabas för utsläpp till luft - Förstudie.

95 Persson, Ch., Robertson L. (SMHI)

Thaning, L (LFOA). (2000) Model for Simulation of Air and Ground Contamination Associated with Nuclear Weapons. An Emergency Preparedness Model.

96 Kindbom K., Svensson A., Sjöberg K.,

(IVL) Persson C., (SMHI) ( 2001) Nationell miljöövervakning av luft- och nederbördskemi 1997, 1998 och 1999.

97 Diamandi, A., Dybbroe, A. (2001)

Nowcasting SAF Validation of AVHRR cloud products.

98 Foltescu V. L., Persson Ch. (2001)

Beräkningar av moln- och dimdeposition i Sverigemodellen - Resultat för 1997 och 1998.

99 Alexandersson, H. och Eggertsson

Karlström, C (2001) Temperaturen och nederbörden i Sverige 1961-1990. Referensnormaler - utgåva 2.

100 Korpela, A., Dybbroe, A., Thoss, A.

(2001) Nowcasting SAF - Retrieving Cloud Top Temperature and Height in Semi-transparent and Fractional Cloudiness using AVHRR.

101 Josefsson, W. (1989)

Computed global radiation using interpolated, gridded cloudiness from the MESA-BETA analysis compared to measured global radiation.

102 Foltescu, V., Gidhagen, L., Omstedt, G.

(2001) Nomogram för uppskattning av halter av PM10 och NO2

103 Omstedt, G., Gidhagen, L., Langner, J.

(2002) Spridning av förbränningsemissioner från småskalig biobränsleeldning – analys av PM2.5 data från Lycksele med hjälp av två Gaussiska spridningsmodeller.

104 Alexandersson, H. (2002)

Temperatur och nederbörd i Sverige 1860 - 2001

105 Persson, Ch. (2002) Kvaliteten hos nederbördskemiska mätdata som utnyttjas för dataassimilation i MATCH-Sverige modellen".

106 Mattsson, J., Karlsson, K-G. (2002) CM-SAF cloud products feasibility study in the inner Arctic region Part I: Cloud mask studies during the 2001 Oden Arctic expedition

107 Kärner, O., Karlsson, K-G. (2003)

Climate Monitoring SAF - Cloud products feasibility study in the inner Arctic region. Part II: Evaluation of the variability in radiation and cloud data

108 Persson, Ch., Magnusson, M. (2003) Kvaliteten i uppmätta nederbördsmängder inom svenska nederbörskemiska stationsnät

109 Omstedt, G., Persson Ch., Skagerström, M (2003) Vedeldning i småhusområden

110 Alexandersson, H., Vedin, H. (2003) Dimensionerande regn för mycket små avrinningsområden

111 Alexandersson, H. (2003) Korrektion av nederbörd enligt enkel klimatologisk metodik

112 Joro, S., Dybbroe, A.(2004) Nowcasting SAF – IOP Validating the AVHRR Cloud Top Temperature and Height product using weather radar data Visiting Scientist report

113 Persson, Ch., Ressner, E., Klein, T. (2004) Nationell miljöövervakning – MATCH-Sverige modellen Metod- och resultatsammanställning för åren 1999-2002 samt diskussion av osäkerheter, trender och miljömål

114 Josefsson, W. (2004) UV-radiation measured in Norrköping 1983-2003.

115 Martin, Judit, (2004) Var tredje timme – Livet som väderobservatör

116 Gidhagen, L., Johansson, C., Törnquist, L. (2004) NORDIC – A database for evaluation of dispersion models on the local, urban and regional scale

117 Langner, J., Bergström, R., Klein, T., Skagerström, M. (2004) Nuläge och scenarier för inverkan på marknära ozon av emissioner från Västra Götalands län – Beräkningar för 1999

118 Trolez, M., Tetzlaff, A., Karlsson, K-G. (2005) CM-SAF Validating the Cloud Top Height product using LIDAR data

119 Rummukainen, M. (2005)

Växthuseffekten 120 Omstedt, G. (2006) Utvärdering av PM10 - mätningar i några olika nordiska trafikmiljöer 121 Alexandersson, H. (2006) Vindstatistik för Sverige 1961-2004

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