Energy balance closure at four forest sites in Wisconsin

Nan LuLEES Lab, University of Toledo

10/27/06

Energy balance closure

Rn = LE+ Hs + G +LE+ Hs + G + Qs

QsQs= Q= Qsoilsoil + Q + Qairair + Q + Qbiomassbiomass

Energy balance Evaluation method: 1. Linear regression coefficient

(slope & intercept) between (LE+Hs) and (Rn-G-Qs) (EBC)

2. Ratio (EBR)

Energy Imbalance! 55-99% at 50 site-years (Wilson

et al., 2002)

Oliphant et al.,2004. AFM

Is Qs important? Qs was typically 5% of Rn in a mature mixed

forest; and it could be up to 10% under some particular conditions, e.g. overcast days, during or immediately following rainfall (McCaughey and Saxton, 1985).

The assessment of the contribution of storage heat to the total energy balance is few for both forest and agricultural ecosystems (Oliphant, 2004; Mayer, 2004) .

What are the conditions under which energy balance is not closed?

The lacks of energy balance closure in the forest were usually identified at night with low friction velocity (u*) (Wilson et al., 2002).

Clouds could play an important role in regulating the energy balance closure by limiting radioactive energy input as well as evaporation (Eltahir and Humphries, 1998; Petrone et al., 2002) .

Effects of forest type? Physical properties of the land surface such as

albedo, roughness and root zone depth affect different components of the energy balance by Rn as well as its partition into Hs and LE (Eltahir and Humphries, 1998).

Objectives 1) Dose heat storage (including Qsoil and

Qair) significantly contribute to the energy balance?

2) Do friction velocity and clouds have effects on energy balance closure?

3) Is energy balance closure different among different forest types?

Study site

23m

26m

9m

3m

Methods

z

sszsoil dzdt

dTCQ

0

)(

Zr

apaa dzdt

dTCQ

0

Zr

paw dz

dt

deCQ

0

Qair=Qa+Qw

(Oliphant et al.,2004. AFM)

Methods: Definition of cloudiness

0

500

1000

1500

2000

2500

0:00 6:00 12:00 18:00 0:00

Time

Day 187

0

500

1000

1500

2000

2500

0:00 6:00 12:00 18:00 0:00

Time

Ph

oto

n d

ensi

ty (

um

ol m

-2 s

-1)

PARPext

Day 186

Comparison of a sunny day (Day 186) and a cloudy day (Day 187) (at IHW, 2003)

Cloudiness=Pext-PARRelative Cloudiness=(Pext-PAR)/Pext

Results

1. Measured energy fluxes (Rn, LE, Hs, G) and storage heat (Qs)

Seasonal variation of LE/Rn, Hs/Rn, G/Rn and Qs/Rn

0

0.03

0.06

0.09

0.12

0.15

May Jun Jul Aug Sep Oct Nov

G/R

n

MRP02 MRP03MHW02 IHW03PB02

0

0.02

0.04

0.06

0.08

May Jun Jul Aug Sep Oct NovMonth

Qs/

Rn

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

May Jun Jul Aug Sep Oct Nov

LE/R

n

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

May Jun Jul Aug Sep Oct NovMonth

Hs/

Rn

0

0.03

0.06

0.09

0.12

0.15

May Jun Jul Aug Sep Oct Nov

G/R

n

MRP02 MRP03MHW02 IHW03PB02

0

0.02

0.04

0.06

0.08

May Jun Jul Aug Sep Oct NovMonth

Qs/

Rn

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

May Jun Jul Aug Sep Oct Nov

LE/R

n

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

May Jun Jul Aug Sep Oct NovMonth

Hs/

Rn

Rn, LE, Hs and G of growing season

-100

0

100

200

300

400

500

600

700

800

0:00 6:00 12:00 18:00 0:00

Time

Rn (

W m

-2)

MRP02MRP03MHW02IHW03PB02

-100

-50

0

50

100

150

200

250

300

0:00 6:00 12:00 18:00 0:00

Time

LE (

W m

-2)

-100

-50

0

50

100

150

200

250

300

0:00 6:00 12:00 18:00 0:00

Time

Hs

(W m

-2)

-30

-20

-10

0

10

20

30

40

50

0:00 6:00 12:00 18:00 0:00

Time

G (

W m

-2)

Comparison of daily variation of Rn, G, Hs, LE among sites, error bar – SE

Comparison of maximum of Rn, LE, Hs and G of growing season among sites

Repeated ANOVA

Site/Yr N Rn LE Hs G

MRP02 650 658.26±7.63 a 165.98±4.12 c 191.92±3.79 a 21.54±0.6 b

MRP03 630 677.69±7.75 a 167.38±4.18 c 201.08±3.85 a 18.02±0.61 c

MHW02 557 582.95±8.24 b 191.42±4.45 b 134.45±4.1 c 15.96±0.65 d

IHW03 578 590.16±8.09 b 234.82±4.37 a 162.11±4.02 b 7.94±0.63 e

PB02 624 527.02±7.79 c 183.99±4.2 b 131.24±3.87 c 35.13±0.61 a

Multiple comparisons of maximum (10:00~12:00 AM) Rn, LE, Hs and G among sites in the growing season

Qs in the growing season

No difference on the daily scale!

Comparison of daily variation of storage heat fluxes (Qs, Qsoil, Qair) among sites, error bar – SE

-40

-20

0

20

40

0:00 6:00 12:00 18:00 0:00

Time

Qair (

W m

-2)

-40

-20

0

20

40

0:00 6:00 12:00 18:00 0:00

Time

Qsoil

(W m

-2)

-40

-20

0

20

40

0:00 6:00 12:00 18:00 0:00

Time

Qs (

W m

-2)

MRP02MRP03MHW02IHW03PB02

Comparison of Qs in different time periods of a day among sites

5<hr<=11 Site/Yr

Qs N Qsoil N Qair N

MRP02 12.89±0.93 c 333 0.63±0.42 c 335 14±0.55 b 969

MRP03 16.2±1.48 b 131 0.79±0.68 c 131 16.04±0.56 a 933

MHW02 19.56±0.64 a 712 3.57±0.29 b 712 16.3±0.61 a 788

IHW03 8.23±0.64 d 694 1.25±0.29 c 698 7.14±0.6 c 823

PB02 10.26±0.67 d 642 7.91±0.3 a 642 2.37±0.59 d 864

17<hr<=23 Site/Yr

Qs N Qsoil N Qair N

MRP02 -13.79±0.87 b 391 -1.8±0.15 a 395 -11.3±0.58 c 980

MRP03 -18.69±1.54 c 124 -1.43±0.26 a 126 -12.56±0.6 c 918

MHW02 -15.53±0.62 bc 779 -3.27±0.11 c 787 -12.02±0.62 c 861

IHW03 -9.03±0.7 a 606 -2.72±0.11 b 702 -6.14±0.68 b 727

PB02 -9.3±0.62 a 781 -7.2±0.11 d 782 -2.03±0.62 a 884

Results

2. Energy balance closure

Contribution of Qs to the energy balance closure

Site/yr MRP02 MRP03 MHW02 IHW03 PB02 Site/yr MRP02 MRP03 MHW02 IHW03 PB02

Slope 0.59 0.65 0.51 0.66 0.68 Slope 0.56 0.55 0.56 0.69 0.65Offset -10.22 -26.86 -17.43 -18.25 -15.40 Offset -0.37 1.75 -0.61 -9.63 -8.75R-square 0.82 0.81 0.81 0.82 0.89 R-square 0.88 0.87 0.85 0.89 0.93

Slope 0.63 0.63 0.60 0.67 0.70 Slope 0.62 0.57 0.59 0.70 0.67Offset -3.26 -3.64 -11.10 -13.25 -13.38 Offset -4.72 4.83 -5.81 -16.07 -13.67R-square 0.86 0.83 0.84 0.82 0.89 R-square 0.90 0.85 0.86 0.90 0.93

Slope 0.46 0.39 0.55 0.79 0.51 slope 0.64 0.57 0.60 0.67 0.67Offset 4.52 6.69 5.60 -0.62 -6.54 offset -10.51 3.00 -11.81 0.85 -13.18R-square 0.55 0.40 0.63 0.63 0.46 R-square 0.82 0.80 0.72 0.77 0.87

Slope 0.44 0.60 0.56 0.81 0.53 slope 0.63 0.56 0.59 0.67 0.67Offset -1.47 2.52 -2.97 -10.23 -12.15 offset -9.56 10.83 -3.81 1.60 -11.45R-square 0.40 0.53 0.74 0.58 0.47 R-square 0.82 0.78 0.67 0.77 0.85

slope 0.61 0.55 0.61 0.71 0.68offset 18.19 25.78 -6.38 -28.16 -10.45R-square 0.75 0.75 0.67 0.66 0.78

Daytime

No Qs

Plus Qs

Site/yr MRP02 MRP03 MHW02 IHW03 PB02 Site/yr MRP02 MRP03 MHW02 IHW03 PB02

Slope 0.59 0.65 0.51 0.66 0.68 Slope 0.56 0.55 0.56 0.69 0.65Offset -10.22 -26.86 -17.43 -18.25 -15.40 Offset -0.37 1.75 -0.61 -9.63 -8.75R-square 0.82 0.81 0.81 0.82 0.89 R-square 0.88 0.87 0.85 0.89 0.93

Slope 0.63 0.63 0.60 0.67 0.70 Slope 0.62 0.57 0.59 0.70 0.67Offset -3.26 -3.64 -11.10 -13.25 -13.38 Offset -4.72 4.83 -5.81 -16.07 -13.67R-square 0.86 0.83 0.84 0.82 0.89 R-square 0.90 0.85 0.86 0.90 0.93

Slope 0.46 0.39 0.55 0.79 0.51 slope 0.64 0.57 0.60 0.67 0.67Offset 4.52 6.69 5.60 -0.62 -6.54 offset -10.51 3.00 -11.81 0.85 -13.18R-square 0.55 0.40 0.63 0.63 0.46 R-square 0.82 0.80 0.72 0.77 0.87

Slope 0.44 0.60 0.56 0.81 0.53 slope 0.63 0.56 0.59 0.67 0.67Offset -1.47 2.52 -2.97 -10.23 -12.15 offset -9.56 10.83 -3.81 1.60 -11.45R-square 0.40 0.53 0.74 0.58 0.47 R-square 0.82 0.78 0.67 0.77 0.85

slope 0.61 0.55 0.61 0.71 0.68offset 18.19 25.78 -6.38 -28.16 -10.45R-square 0.75 0.75 0.67 0.66 0.78

No Qs at 5<hour<=11

Plus Qs at 5<hour<=11

No Qs at 17<hour<=23

Plus Qs at 17<hour<=23

All day

Two particular time periods

Energy balance closure under different conditions

0.20

0.40

0.60

0.80CloudySunny

0.20

0.40

0.60

0.80u<u* u>u*

0.2

0.4

0.6

0.8

Slo

pe

NoctualDaytime

-35.00

-15.00

5.00

25.00

-35.00

-15.00

5.00

25.00

-35

-15

5

25

Off

set

0.000.20

0.400.60

0.801.00

MR

P02

MR

P03

MH

W02

IHW

03

PB

02

0.000.20

0.400.60

0.801.00

MR

P02

MR

P03

MH

W02

IHW

03

PB

020

0.2

0.40.6

0.81

MR

P02

MR

P03

MH

W02

IHW

03

PB

02

R-s

qu

are

Energy balance closure under different conditions

All data available

Site/yr MRP02 MRP03 MHW02 IHW03 PB02 Site/yr MRP02 MRP03 MHW02 IHW03 PB02

Slope 0.59 0.65 0.51 0.66 0.68 Slope 0.56 0.55 0.56 0.69 0.65Offset -10.22 -26.86 -17.43 -18.25 -15.40 Offset -0.37 1.75 -0.61 -9.63 -8.75R-square 0.82 0.81 0.81 0.82 0.89 R-square 0.88 0.87 0.85 0.89 0.93

Slope 0.63 0.63 0.60 0.67 0.70 Slope 0.62 0.57 0.59 0.70 0.67Offset -3.26 -3.64 -11.10 -13.25 -13.38 Offset -4.72 4.83 -5.81 -16.07 -13.67R-square 0.86 0.83 0.84 0.82 0.89 R-square 0.90 0.85 0.86 0.90 0.93

Slope 0.46 0.39 0.55 0.79 0.51 slope 0.64 0.57 0.60 0.67 0.67Offset 4.52 6.69 5.60 -0.62 -6.54 offset -10.51 3.00 -11.81 0.85 -13.18R-square 0.55 0.40 0.63 0.63 0.46 R-square 0.82 0.80 0.72 0.77 0.87

Slope 0.44 0.60 0.56 0.81 0.53 slope 0.63 0.56 0.59 0.67 0.67Offset -1.47 2.52 -2.97 -10.23 -12.15 offset -9.56 10.83 -3.81 1.60 -11.45R-square 0.40 0.53 0.74 0.58 0.47 R-square 0.82 0.78 0.67 0.77 0.85

slope 0.61 0.55 0.61 0.71 0.68offset 18.19 25.78 -6.38 -28.16 -10.45R-square 0.75 0.75 0.67 0.66 0.78

No Qs

Site/yr MRP02 MRP03 MHW02 IHW03 PB02 Site/yr MRP02 MRP03 MHW02 IHW03 PB02

Slope 0.59 0.65 0.51 0.66 0.68 Slope 0.56 0.55 0.56 0.69 0.65Offset -10.22 -26.86 -17.43 -18.25 -15.40 Offset -0.37 1.75 -0.61 -9.63 -8.75R-square 0.82 0.81 0.81 0.82 0.89 R-square 0.88 0.87 0.85 0.89 0.93

Slope 0.63 0.63 0.60 0.67 0.70 Slope 0.62 0.57 0.59 0.70 0.67Offset -3.26 -3.64 -11.10 -13.25 -13.38 Offset -4.72 4.83 -5.81 -16.07 -13.67R-square 0.86 0.83 0.84 0.82 0.89 R-square 0.90 0.85 0.86 0.90 0.93

Slope 0.46 0.39 0.55 0.79 0.51 slope 0.64 0.57 0.60 0.67 0.67Offset 4.52 6.69 5.60 -0.62 -6.54 offset -10.51 3.00 -11.81 0.85 -13.18R-square 0.55 0.40 0.63 0.63 0.46 R-square 0.82 0.80 0.72 0.77 0.87

Slope 0.44 0.60 0.56 0.81 0.53 slope 0.63 0.56 0.59 0.67 0.67Offset -1.47 2.52 -2.97 -10.23 -12.15 offset -9.56 10.83 -3.81 1.60 -11.45R-square 0.40 0.53 0.74 0.58 0.47 R-square 0.82 0.78 0.67 0.77 0.85

slope 0.61 0.55 0.61 0.71 0.68offset 18.19 25.78 -6.38 -28.16 -10.45R-square 0.75 0.75 0.67 0.66 0.78

Daytime&u>u*&sunny

Daytime

Daytime&u>u*

Discussion

-100

100

300

500

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900

-200 200 600 1000 1400 1800

Pext-PAR (umol m-2 s-1)

W m

-2

LE

Hs

-100

100

300

500

700

900

0 0.5 1 1.5 2 2.5 3 3.5

Log (Pext-PAR)

LE

+Hs

(W m

-2)

Discussion

-3

-2

-1

0

1

2

3

4

-200 0 200 400 600 800

LE+Hs (W m-2)

EB

R

Linear regression between EBC and the canopy height (account for Qs and not account for Qs)

y = -0.0049x + 0.6788R2 = 0.8379

y = -0.0042x + 0.6971R2 = 0.7576

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0 5 10 15 20 25 30

Canopy height (m)

Slo

pe

No S Include SQs Qs

EB

C

Conclusions 1. Net radiation and its portioning to LE, Hs

and G were different at half-hourly scale among sites; largest difference occurred around noon. But there was not a difference in Qs among sites.

2. Qs was different among sites during the hours after dawn and around dusk when Qs was a larger proportion of Rn. Storage was greater in the taller than shorter canopies.

Conclusions 3. Storage energy improved the energy

balance closure by 1-6% at of our study sites; during the particular time periods of dawn and dusk, Qs could increased energy balance closure by 9-11% for tall canopies.

4. Energy balance closure was higher when friction velocity was greater and the sky was clearer.