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1 Institute for Meteorology and Climate Research IMK-IFU Integration of Remote Sensing Information in Hydrological Models Harald Kunstmann Institute for Meteorology and Climate Research IMK-IFU Garmisch-Partenkirchen Email: [email protected]

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1 Institute for Meteorology and Climate Research IMK-IFU

Integration of Remote Sensing Information in

Hydrological Models

Harald KunstmannInstitute for Meteorology and Climate Research IMK-IFU

Garmisch-Partenkirchen

Email: [email protected]

2 Institute for Meteorology and Climate Research IMK-IFU

Institute for Meteorology and Climate Research, Garmisch-Partenkirchen

3 Institute for Meteorology and Climate Research IMK-IFU

Institute for Meteorology and Climate Research, Garmisch-Partenkirchen

4 Institute for Meteorology and Climate Research IMK-IFU

Motivation Hydrology: Water, Men and Environment

Worldwater

• Precipitation over land: 110,000 km³/a (cube with ∆x=48km)

• Evapotranspiration: 50,000 km³/a natural vegetation (∆x=37km)18,000 km³/a rainfed agriculture (∆x=26km)

• Rivers: 42,000 km³/a (∆x=35km)⇒ but only 13,000 km³/a accessible for humans (∆x=23km)⇒ 2,000 km³/a for irrigation (∆x=12km)

• Groundwater extraction 800 km³/a, thereof 200 km³/a non sustainable (fossil)

⇒ Evaporation water agriculture ≈ ½ evaporation natural vegetation

5 Institute for Meteorology and Climate Research IMK-IFU

Motivation Hydrology: Water, Men and Environment

Worldwater

World freshwater consumption

Agricultu

re

5000 km³/a

⅓ till ½ of worldwide accessible freshwater resources are already used!

6 Institute for Meteorology and Climate Research IMK-IFU

Water: more than H2O

Flooding Water Scarcity

7 Institute for Meteorology and Climate Research IMK-IFU

Remote Sensing in Hydrology

Remote sensing produces • Areal/line measurements in place of point measurements• all information is collected & stored at one place • it offers high resolution in space and/or time • data are available in digital form • …

Remote sensing platforms • Station based (RADAR, LIDAR)• Satellites• Airborne

8 Institute for Meteorology and Climate Research IMK-IFU

Overview

Station based: examples • Radar (Radio detection and ranging) areal estimation of precipitation

Weilheim

Staffelsee

Oberammergau

Radar

Hohenpeißenberg

9 Institute for Meteorology and Climate Research IMK-IFU

Overview

Station based: examples • Radar (Radio detection and ranging) areal estimation of precipitation• LIDAR (Light detection and ranging ): e.g. water vapor

10 Institute for Meteorology and Climate Research IMK-IFU

Overview

Station based: examples • Radar (Radio detection and ranging) areal estimation of precipitation• LIDAR (Light detection and ranging ): e.g. water vapor• Cellular network microwave attenuation: line integral of precipitation

Comparison of the time series of rainfall intensity measured bycellular links, rain gauges, and a weather radar, in two areas in Israel: (A) Tel-Aviv and (B) Haifa (Messer et al., 2006)

Virtual Institute PROCEMA, PhD Wei Qiu, ESPACE MSc. graduate in 2008

11 Institute for Meteorology and Climate Research IMK-IFU

Satellite based: examples1) Radar Systems (active)

• independent of cloud cover & daytime• observation of e.g. soil moisture• satellites SMOS (60x60 km², ∆t=3 days)

ENVISAT ASAR (up to150x150m²)Terra-SAR-X (up to 1x1m²)TRMM (0.25x0.25°)

2) Multi- and Hyperspectral Sensors (passive) • observation of e.g. surface temperatures • vegetation & snow cover dynamics• heat fluxes, using Energy Balance Models, e.g. SEBAL• satellites: e.g. NOAA-AVHRR, MODIS, Landsat

3) others: e.g. GRACE

MODIS SMOSGRACE TERRA-SARLandsatEnvisat

Overview

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Basics of Hydrological Modelling

The Hydrological Cycle

13 Institute for Meteorology and Climate Research IMK-IFU

Basics of Hydrological ModellingTerrestrial Water Balance & Runoff components

Interflow qi

Direct Runoff qdir

Groundwater/Base Flow qbas

Evapotranspiration ETr

Precipitation P

14 Institute for Meteorology and Climate Research IMK-IFU

Basics of Hydrological Modelling

Water and Energy Fluxes at Land Surface

P

ET

R

∆S ⇐

Soil-Vegetation-Atmosphere-Transfer (SVAT) Model

15 Institute for Meteorology and Climate Research IMK-IFU

Flächendifferenzierte Wasserhaushaltsmodellierung

EvapotranspirationInfiltration

Groundwater

Flow

])([]1)[(])[(

γλρλργ+

−++=

avw

asatavwEa

TsRHTevKLKTsE

thSR

zhK

zyhK

yxhK

x shzhyhx ∂∂

−=+⎟⎠⎞

⎜⎝⎛

∂∂

∂∂

−⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

∂∂

−⎟⎠⎞

⎜⎝⎛

∂∂

∂∂

2/1

, 11)(⎥⎥⎥

⎢⎢⎢

⎟⎟

⎜⎜

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛−−

−−−−

=

mm

res

res

res

ressathh KK

θφθθ

θφθθθ

tzK

zK

zh

h ∂∂

=∂

∂−⎟⎠⎞

⎜⎝⎛

∂Ψ∂

∂∂ θθθθ

')(

')()(

'

Routing Wave retention

I

BvQB

vQMv

hh

hh

hhh

3/2

2/

⎟⎟⎟⎟

⎜⎜⎜⎜

+=

Basics of Hydrological Modelling

HydraulicConductivity

∆x, ∆y = 100m-1km, ∆t =1h-1d

16 Institute for Meteorology and Climate Research IMK-IFU

Example 1: Radar & Precipitation

17 Institute for Meteorology and Climate Research IMK-IFU

Integration of Radar Derived Precipitation

Radar

Hohenpeißenberg

Wavelength ~ 5 cm (C-Band)

Scanning in 1°-wide sectors

Measuring of backscattered signal Z, which is related to precipitation R:

Z = a × Rb

Z Reflektivity factor [mm6m-3] R Rain intensity [mm/h]a, b Empirical constants (DWD-Standard 256,1.42)

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Integration of Radar Derived Precipitation

3-dimensional scanning (volume scan) in 15 min

Rainscan (lowest elevation) every 5 minutes

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Integration of Radar Derived Precipitation

Case Study: Catchment of the River Ammer

Weilheim

Oberhausen

Peissenberg

Obernach

Unternogg

O’gau

Munich

Garmisch

Innsbruck

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Integration of Radar Derived Precipitation

Ammer Catchment

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Integration of Radar Derived Precipitation

• Location: Southern Bavaria / Germany

• Area: 710 km2

• Alpine/Prealpine environment

• Complex orography

• Elevation: 530-2190m above sea level

• Mean precipitation: 1400 mm/a (67% in summer)

• Days with snow cover: 127/a

• Temperature gradient: ≈ 0.6 °C/100m

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Basics of Hydrological Modelling

Hydrological Model WaSiM

http://www.wasim.ch

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Basics of Hydrological Modelling

Special features WaSiM (incomplete):

• Variable cell sizes• Dynamic simulation of vegetation development (LAI Dynamics)• Advanced landuse table• Advanced soil table• Macropore runoff• Exfiltration and re-infiltration of groundwater• Irrigation management• Considering (artificial) drainage• Considering ponds• Modelling of glacier runoff• Considering reservoir management• Considering external abstractions and inflows• Online coupling with external models• Coupling of sequential model runs• Coupling of substance transport ( tracer) with water flow

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Integration of Radar Derived Precipitation

Gauge 6 (Peißenberg)

0

1

2

3

4

5

6

7

8

9

10

Nov-96 Dec-96 Dec-96 Jan-97 Mar-97 Mar-97 Apr-97 May-97 Jun-97 Jul-97 Aug-97 Sep-97 Oct-97

Spec

ific

Dis

char

ge [m

m/8

h]

0

5

10

15

20

25

30

35

40

45

50

Prec

ipita

tion

[mm

/8h]

precipitation simulated modelliert

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Integration of Radar Derived Precipitation

Interpolated Precipitation RadarIDW+Regression IDW

Weilheim

Ettal

Precipitation [mm/h] in Ammer-catchment, 17.07.2001, 15.00 UTC

26 Institute for Meteorology and Climate Research IMK-IFU

Integration of Radar Derived Precipitation

Spe

cific

Dis

char

ge [m

m/h

] observed q simulated q

Gauge Halbammer

Summer 2001

• Erroneous precipitation interpolation yields fictitious runoff events• Automatic calibration seeks compensation via adjustment ofparameters does not yield optimal parameter set

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Radar raw data: dBZ-time series

Clutter Zugspitze

Clutter City Munich

Zugspitze

MoHP: 3-min-data Munich: 5-min-data

Integration of Radar Derived Precipitation

Data characteristics dependent on radar type and data processing

28 Institute for Meteorology and Climate Research IMK-IFU

Integration of Radar Derived Precipitation

PE=K × PS(ε/(λ4 × R2)) ∑ N × d6 [W]

PE Received powerPS Emitted powerε Dielectric constantλ Wavelength of Radar radiationR Distance radar station - objectd Diameter precipitation dropletsN Number precipitation dropletsK Constant from parameters of radar device

Z

Problem of non-uniqueness:Example: Z =∑ N × d6 = 1×56 = 729×36 = 15625×16

29 Institute for Meteorology and Climate Research IMK-IFU

Integration of Radar Derived Precipitation

Z = a × Rb

Z Reflectivity factor [mm6m-3] R Rain intensity [mm/h]a,b Empirical constants (DWD-Standard 256,1.42)

3-part Z/R-relation (RADOLAN-Projekt)

dBZ < 36.5 36.5 … 44 > 44

a 125 200 77

b 1.4 1.6 1.9

New calibration method2 transitions c, 3 coefficient pairs a,b

30 Institute for Meteorology and Climate Research IMK-IFU

Integration of Radar Derived Precipitation

Assimilation/Integration of Radar Data in WaSiM

• Spatial position of Radar points of MoHP device

• ∆x~1km

• Every gridpoint complies with a fictitious met. station in WaSiM

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Integration of Radar Derived Precipitation

Coefficients Z/R-Relation

Iterative Calibration of a Q-Z/R-Relation

1. c1,c2 2. a1,b1 3. a2,b2 4. a3,b3

Hourly Radar precipitation

data

Hydrological Simulation

Nash-Sutcliffe criteriumfor 5 subcatchments

Runoff observations

32 Institute for Meteorology and Climate Research IMK-IFU

Integration of Radar Derived Precipitation

Result: Derived Q-Z/R-Relation

dBZ < 36 36 …44.5 > 44.5

a 104 131 73

b 1.43 1.57 1.63

Yields best results for hydrological simulations of 5 subcatchments

robust relation for hydrological modeling of Ammer catchment

33 Institute for Meteorology and Climate Research IMK-IFU

Integration of Radar Derived PrecipitationQ-Z/R – Comparison with station data [~mm/8h]

34 Institute for Meteorology and Climate Research IMK-IFU

Integration of Radar Derived PrecipitationQ-Z/R – Validation

Station data Station data

Rad

arda

ten

Rad

arda

ten

Underestimation minimized in comparison to station data

35 Institute for Meteorology and Climate Research IMK-IFU

Integration of Radar Derived Precipitation

36 Institute for Meteorology and Climate Research IMK-IFU

Integration of Radar Derived PrecipitationComparison of differently derived precipitation fields

MOHp

Bad Kohlgrub

IDW Radar (Q-Z/R) Ordinary Kriging

Precipitation sum 17.-21.06.2001 [mm]

37 Institute for Meteorology and Climate Research IMK-IFU

Integration of Radar Derived Precipitation

Blue:

Radar data gaps

38 Institute for Meteorology and Climate Research IMK-IFU

Integration of Radar Derived Precipitation

Blue:

Radar data gaps

39 Institute for Meteorology and Climate Research IMK-IFU

Integration of Radar Derived Precipitation

Summary

• Derivation of Q-Z/R-relation based on discharge measurements and calibrated hydrological model

• Radar driven continuous hydrological simulation over 3 months period yield reasonable good results

• Adaptation of Q-Z/R-relation yields minimisation/reduction of (Radar typical-) underestimation compared to station data

40 Institute for Meteorology and Climate Research IMK-IFU

Example 2: MODIS & Land Surface Properties

41 Institute for Meteorology and Climate Research IMK-IFU

The Volta Basin of West Africa

42 Institute for Meteorology and Climate Research IMK-IFU

Scientific. Sound Decision Support under Weak Infrastructure

43 Institute for Meteorology and Climate Research IMK-IFU

White Volta Catchment

• White Volta: 94,000 km², upstream of Lake Volta

• Flat topography

• Semi arid climate: Rainy season May - October Dry season November – April

Jung, 2006

44 Institute for Meteorology and Climate Research IMK-IFU

Integration of MODIS Derived Land Surface Data

For hydrological modeling in poorly gauged basins & regions with a weak infrastructure (White Volta basin)

• Remote sensing (RS) is valuable data source - RS satisfies several data requirements - RS provides data near real time!

no delay due to data collection, digitalization,…

In this study

• RS products are used for a better description of land surface parameters in hydrological modeling

• Land surface properties albedo & LAI (Leaf Area Index) from the space-borne remote sensing system MODIS are employed

Integration of MODIS derived land surface properties into a water balance simulation model ( WaSiM)

45 Institute for Meteorology and Climate Research IMK-IFU

Integration of MODIS Derived Land Surface Data

Digital Elevation Model

∆x=1km, ∆t=1d

46 Institute for Meteorology and Climate Research IMK-IFU

Integration of MODIS Derived Land Surface DataDEM Soil grid Land Use grid

+ Tables with Soil and Land Use properties

Code Name Albedosurface

resistance DOY's LAIveg.

height veg.

coveringroot

depth[monthly] 1 … 4 1 …4 1 …4 1 …4 1 …4

8 shrubland

19 bar.sparse.veg.

Example: Land Use Table

47 Institute for Meteorology and Climate Research IMK-IFU

Integration of MODIS Derived Land Surface Data

• Satellite derived: MODIS

• Satellites provide worldwide spatially information on land surface properties

(e.g. MODIS entire earth every 2 days)

• Advantages:

- more detailed spatial and temporal description of land surface variables

- one data source

- allows inter-annual investigations

- …

48 Institute for Meteorology and Climate Research IMK-IFU

Integration of MODIS Derived Land Surface Data

• http://modis.gsfc.nasa.gov/index.php

49 Institute for Meteorology and Climate Research IMK-IFU

Integration of MODIS Derived Land Surface Data

• http://modis.gsfc.nasa.gov/index.php

• Moderate Resolution Imaging Spectroradiometer

• Terra (EOS AM) & Aqua (EOS PM) satellites

• global coverage within 1 to 2 days

• 36 spectral bands: 0.4 – 14 µm

• goal: improve understanding of global dynamics & processes on land, oceans, lower atmosphere

• 44 data products (250 – 1000 m)

50 Institute for Meteorology and Climate Research IMK-IFU

MODIS – 44 data products

Integration of MODIS Derived Land Surface Data

51 Institute for Meteorology and Climate Research IMK-IFU

Integration of MODIS Derived Land Surface Data

MODIS LAND: • MOD 43: Surface Reflectance BRDF/Albedo

Parameter - spatial resolution: 1km- temporal resolution: 16 days

• MOD 15: Leaf Area Index (LAI) and Fractional Photosynthetically Active Radiation (FPAR)- spatial resolution: 1km- temporal resolution: 8 days

52 Institute for Meteorology and Climate Research IMK-IFU

Potential evapotranspiration

α

• Definition: maximum quantity of water capable of being evaporated from the soil to the atmosphere by evaporation and plant transpiration of a specified region (climate)

• Penman-Monteith:

with

and

• Albedo

• LAI Leaf Area Index

53 Institute for Meteorology and Climate Research IMK-IFU

Potential evapotranspiration

• List of symbols

54 Institute for Meteorology and Climate Research IMK-IFU

Potential evapotranspiration

• ra: aerodynamic resistance• rs: bulk surface resistance

http://www.fao.org/docrep/x4090/x4090e06.htm

55 Institute for Meteorology and Climate Research IMK-IFU

Potential evapotranspirationSurface Albedo [ ]

• Definition: reflectance of incident energy by the surface; determined by surface reflectance properties, which vary for different forms of surface materials and wetness

• Penman-Monteith:

with

• Increase of values Decrease ofα Eλ

56 Institute for Meteorology and Climate Research IMK-IFU

LAI: Leaf Area Index [ ]

• Definition: total one-sided leaf area per unit ground surface

• Penman-Monteith:

with

Increase of LAI values Increase of

Potential evapotranspiration

EλLAI

57 Institute for Meteorology and Climate Research IMK-IFU

Integration of MODIS Derived Land Surface Data

Seasonal cycle for the White Volta basin

58 Institute for Meteorology and Climate Research IMK-IFU

Integration of MODIS Derived Land Surface Data

standard literaturealbedo depending on LU type

MODIS 3 month-mean 2004 Jan-Mar Oct-Dec

Jul-SepApr-Jun

59 Institute for Meteorology and Climate Research IMK-IFU

Integration of MODIS Derived Land Surface Data

MODIS 3 month-mean Jan-Mar Oct-Dec

Jul-SepApr-Jun

MODIS:

Latitudinal profile of monthly means

60 Institute for Meteorology and Climate Research IMK-IFU

2004Jan-Mar Oct-Dec

Jul-SepApr-Jun

Albedo inter-annual variability: MODIS 2004 & 20052005

Jan-Mar Oct-Dec

Jul-SepApr-Jun

Integration of MODIS Derived Land Surface Data

61 Institute for Meteorology and Climate Research IMK-IFU

Integration of MODIS Derived Land Surface Data

Standard literatureLAI depending on LU type

MODIS 3 month-mean 2004 Jan-Mar Oct-Dec

Jul-SepApr-Jun

dry season:

rainy season:

Nov-Apr

May-Oct

62 Institute for Meteorology and Climate Research IMK-IFU

Integration of MODIS Derived Land Surface Data

MODIS 3 month-mean 2004 Jan-Mar Oct-Dec

Jul-SepApr-Jun

MODIS 2004:

Latitudinal profile of monthly means

63 Institute for Meteorology and Climate Research IMK-IFU

2004Jan-Mar Oct-Dec

Jul-SepApr-Jun

LAI: Inter-annual variability: MODIS 2004 & 20052005

Jan-Mar Oct-Dec

Jul-SepApr-Jun

Integration of MODIS Derived Land Surface Data

64 Institute for Meteorology and Climate Research IMK-IFU

Impact of MODIS albedo and LAI on water balance estimations

a) time series of spatially aggregated variables

b) spatial distribution of annual sums

65 Institute for Meteorology and Climate Research IMK-IFU

Integration of MODIS Derived Land Surface Data

Eta [mm]2004:

ETp [mm]

Qtotal [mm]

legend: Control-RunMODIS Albedo MODIS LAI MODIS Albedo & LAI

66 Institute for Meteorology and Climate Research IMK-IFU

Inter-annual VariabilityETp [mm]

2004: 2005:

Integration of MODIS Derived Land Surface Data

Legend: Control-RunMODIS Albedo MODIS LAI MODIS Albedo & LAI

67 Institute for Meteorology and Climate Research IMK-IFU

ETa [mm]2004: 2005:

Integration of MODIS Derived Land Surface Data

Legend: Control-RunMODIS Albedo MODIS LAI MODIS Albedo & LAI

68 Institute for Meteorology and Climate Research IMK-IFU

Integration of MODIS Derived Land Surface Data

Qtotal [mm]2004: 2005:

Legend: Control-RunMODIS Albedo MODIS LAI MODIS Albedo & LAI

69 Institute for Meteorology and Climate Research IMK-IFU

Integration of MODIS Derived Land Surface Data

Annual sums of potential ET

MODIS LAIMODIS

Albedo & LAIMODIS AlbedoCTR

2004:

[mm]

70 Institute for Meteorology and Climate Research IMK-IFU

Integration of MODIS Derived Land Surface Data

MODIS Albedo MODIS LAI

Differences of annual sums of potential ETwith respect to simulations using static tabulated values

[mm

]

MODIS Albedo & LAI

2004:

71 Institute for Meteorology and Climate Research IMK-IFU

Integration of MODIS Derived Land Surface Data

Differences of annual sums – MODIS Albedo & LAIwith respect to simulations using static tabulated values

[mm

]

∆Qtotal∆ETa∆ETp

2004:

72 Institute for Meteorology and Climate Research IMK-IFU

Integration of MODIS Derived Land Surface Data

∆ETa ∆Qtotal∆ETp

[mm

]Differences of annual sums – MODIS Albedo & LAI

with respect to simulations using static tabulated values2004:

total basin: +2% +1%

-2% – +5% -4% – +7%

-1%

sub basin: -26% – +35%*

73 Institute for Meteorology and Climate Research IMK-IFU

Integration of MODIS Derived Land Surface Data

Inter-annual variability: Annual sums – MODIS Albedo & LAI

ETp: 2004 2005

74 Institute for Meteorology and Climate Research IMK-IFU

Integration of MODIS Derived Land Surface Data

Inter-annual variability: Differences of annual sums – MODIS Albedo & LAIwith respect to simulations using static tabulated values

∆ETp: 20052004

75 Institute for Meteorology and Climate Research IMK-IFU

Integration of MODIS Derived Land Surface Data

Inter-annual variability:Differences of annual sums – MODIS Albedo & LAI

with respect to simulations using static tabulated values

∆ETa: 2004 2005

76 Institute for Meteorology and Climate Research IMK-IFU

Integration of MODIS Derived Land Surface Data

Inter-annual variability:Differences of annual sums – MODIS Albedo & LAI

with respect to simulations using static tabulated values

∆Qtotal: 2004 2005

77 Institute for Meteorology and Climate Research IMK-IFU

2004 2005

ETp ETa Qtotal

Tabulated 1879 770 81MODIS ALB 1961 785 79MODIS LAI 1851 763 81MODIS ALB & LAI 1916 779 80

ETp ETa Qtotal

Tabulated 1966 734 85MODIS ALB 2035 741 83MODIS LAI 1926 739 83MODIS ALB & LAI 1962 744 81

ETp ETa Qtotal

Tabulated 214 83 66MODIS ALB & LAI 173 80 62

ETp ETa Qtotal

Tabulated 234 87 60MODIS ALB & LAI 193 82 57

Annual sums:

Standard deviation within subcatchments:

Integration of MODIS Derived Land Surface Data

78 Institute for Meteorology and Climate Research IMK-IFU

Integration of MODIS Derived Land Surface Data

Summary

• Integration of MODIS albedo & LAI into a hydrological model

• Comparison MODIS albedo & LAI versus standard literature values - albedo: increased level of detail in spatial dimension - LAI: additional better representation of temporal development

• MODIS application allows inter-annual comparisons - further advantage: all data are based on same data source & time

• Impact of MODIS albedo & LAI on hydrological simulation results- minor on daily time series of spatially aggregated variables - clear on spatial distribution of water balance variables

79 Institute for Meteorology and Climate Research IMK-IFU

Thanks to Andreas Marx and Sven Wagner

andthank you for your attention

80 Institute for Meteorology and Climate Research IMK-IFU

Short Example: Areal Validation of Heat Fluxes

0

120

240

[Wm-2]

NOAA-AVHRR & SEBAL-Algorithm

Satellite (7 Overflights) vs. Scintillometer dataBars: Uncertainties from Gaussian Error Propagation

Sensible Heat Flux (H), 14.12.2001

81 Institute for Meteorology and Climate Research IMK-IFU

Short Example: Large Scale Water Balance

Tom

Jerry

PETQt

Wa −=⋅∇+

∂∂

dtdSRQ ≈−⋅∇ )(

WRF vs. GRACE Observation of gravity/acceleration

82 Institute for Meteorology and Climate Research IMK-IFU

Integration of Radar Derived Precipitation

Processing of Radar data

Radarreflektivity 3-min Cluttermask400 rainfree scenes

83 Institute for Meteorology and Climate Research IMK-IFU

Integration of Radar Derived Precipitation

Radar Reflectivity 3-min [Z] Cluttermask [Z]

Radar Precipitation 3-min

Computation Hourly PrecipitationCorrecting of missing scenes

Z/R-Relation

Radar Precipitation [mm/h]

84 Institute for Meteorology and Climate Research IMK-IFU

Integration of Radar Derived Precipitation

Error sources

Jordan et al., 2003

85 Institute for Meteorology and Climate Research IMK-IFU

Integration of MODIS Derived Land Surface Data

Water and Energy Fluxes at Land Surface

Soil-Vegetation-Atmosphere-Transfer (SVAT) Model

P

ET

R

∆S ⇐LK

LWLWSWLWLWSWSWR

outinin

outinoutinn

+=⇒−+−=−+−=

)1( α GHEAPGHER dn

++≈≈++++=

λλ

GHETLWSW sfcinin ++≈−+− λσεα 4)1(Albedo