Opened 8 years ago

Closed 7 years ago

# Incorrect formula in snow albedo

Reported by: Owned by: mmcgrath cottle minor ORCHIDEE 1.9.7 Physical processes orchidee_1_9_6 Snow, albedo

### Description

It seems to me that there is a small problem with one of the formulas currently used. In particular, it doesn't match with the formula in the reference. In Chalita and Le Treut (1994), Eq. 1 gives the formula for calculating the fraction of the snow cover for a grid square.

beta=eta/(eta+eta_c)

where eta_c, the critical snow depth, is 10 cm, and eta is the snow
depth in centimeters. In ORCHIDEE, a similar formula is used in
condveg_snow

```     frac_snow_veg(:) = MIN(MAX(snow(:),zero)/(MAX(snow(:),zero)+snowcri_alb),un)
DO jv = 1, nnobio
frac_snow_nobio(:,jv) = MIN(MAX(snow_nobio(:,jv),zero)/(MAX(snow_nobio(:,jv),zero)+snowcri_alb),un)
ENDDO
```

except that here, snowcri_alb is given as 10 kg/m2, and snow is the snow mass also given in kg/m2. The difference in units means that the critical parameter is not the same in the two equations. If I change the units so they are the same, the total albedo changes slightly.

I propose that either the units of snowcri_alb are changed to kg/m2 by multiplying by sn_dens and dividing by 100, or the units of snow in this subroutine are changed to cm by dividing by sn_dens and multiplying by 100. Both suggestions produce the same results, and can be achieved by the following change in condveg_snow. The above section should be changed to either

```    frac_snow_veg(:) = MIN(MAX(snow(:),zero)/(MAX(snow(:),zero)+snowcri_alb*sn_dens/100.0),un)
DO jv = 1, nnobio
frac_snow_nobio(:,jv) = MIN(MAX(snow_nobio(:,jv),zero)/(MAX(snow_nobio(:,jv),zero)+snowcri_alb*sn_dens/100.0),un)
ENDDO
```

or

```    frac_snow_veg(:) = MIN(MAX(snow(:)/sn_dens*100.0,zero)/(MAX(snow(:)/sn_dens*100.0,zero)+snowcri_alb),un)
DO jv = 1, nnobio
frac_snow_nobio(:,jv) = MIN(MAX(snow_nobio(:,jv)/sn_dens*100.0,zero)/(MAX(snow_nobio(:,jv)/sn_dens*100.0,zero)+snowcri_alb),un)
ENDDO
```

In addition, the declaration of snowcri_alb can be changed, but this way seems to be more flexible in case the snow density changes in the future.

An example run is attached which illustrates the changes in the NIR albedo during the winter months in a temperate forest.

### Changed 8 years ago by mmcgrath

A graph of the total albedo in the NIR regime as a funcation of time for using the existing (old) and corected (new) snow albedo formula

### comment:1 Changed 8 years ago by nvuilsce

• Owner changed from somebody to cottle
• Status changed from new to assigned

### comment:2 Changed 7 years ago by cottle

• Status changed from assigned to accepted

### comment:3 Changed 7 years ago by jgipsl

• Resolution set to fixed
• Status changed from accepted to closed

Done rev 

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