STRENGTH AND TEMPORAL EVOLUTION OF THE LAND - ATMOSPHERE COUPLING IN THE MURRAY- DARLING BASIN

Philippe Steer [email protected]

August 2006

Figure 1: Pictures of the Murray-Darling Basin ©ABC Training of first year of Master Sciences de l’Univers, Environnement, Ecologie (Ecole Normale Sup´erieure, Paris 6). Undertaken at the Bureau of Meteorology Research Centre (Melbourne, Australia), supervised by Bryant McAvaney and Bertrand Timbal.

Abstract This study aims to describe and to quantify the coupling between land and atmosphere in the semiarid Murray-Darling Basin. The methodology used is similar to the one described by A. Betts [Betts, 2004] and used in the Amazon Basin [Betts and Viterbo, 2005]. The climatology and the coupling between land and atmosphere are not the same between re-analyses, between GCMs, and between re-analyses and GCMs. Nevertheless it is remarkable that for each re-analysis the land-atmosphere coupling is weaker in the Murray-Darling than in the Amazon Basin. The sensitivity of the Murray-Darling Basin to external forcings is high as it is a dry area. It results that the signal coming from the internal coupling between land and atmosphere is strongly disrupted by external influences in the Murray-Darling Basin. The integration time step is a parametre that also need to be taken into account, as statistical links between atmosphere and land variables are strongly dependent on it. This dependency has a major impact on statistical links between soil moisture and precipitation. Climate change does not radically disrupt soil moisture-precipitation feedback and more generally land-atmosphere interactions. Cette e´ tude a pour objectifs la description et la quantification du couplage entre la surface du sol et l’atmosph`ere dans le bassin du MurrayDarling. La m´ethode utilis´ee est celle pr´econis´ee par A. Betts [Betts, 2004] appliqu´ee ensuite au bassin de l’Amazone [Betts and Viterbo, 2005]. La climatologie et par cons´equent le couplage entre le sol et l’atmosph`ere ne sont pas identique entre les re-analyses, entre les GCMS, et entre les re-analyses et les GCMs. De plus nous avons constat´e que ce couplage est plus faible dans le bassin du Murray-Darling que dans celui de l’Amazone. En effet la sensitivit´e du bassin du Murray-Darling aux influences externes est e´ lev´ee du fait de son aridit´e. Par cons´equent le signal provenant du couplage dans le bassin est fortement perturb´e. Les relations statistiques entre les variables de l’atmosph`ere et celles du sol d´ependent fortement du pas temporel d’int´egration utilis´e. La vision du couplage entre l’eau du sol et les pr´ecipitations est radicalement diff´erente selon le pas de temps utilis´e. Enfin le changement climatique ne perturbe pas consid´erablement les interactions entre le sol et l’atmosph`ere comme par exemple la r´etroaction de l’eau du sol sur les pr´ecipitations.

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Contents 1 Introduction

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2 Presentation, state of the art and methodology 2.1 The Murray-Darling Basin . . . . . . . . . . . . . . . . . . . . . 2.1.1 Geographical presentation . . . . . . . . . . . . . . . . . 2.1.2 Climate and natural environments . . . . . . . . . . . . . 2.1.3 Economic activities linked with climat and hydrology . . . 2.1.4 Environmental and Hydrological issues . . . . . . . . . . 2.2 Available Database . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Observations: . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2 Outputs from re-analysis: . . . . . . . . . . . . . . . . . . 2.2.3 Outputs from CAOGCms: . . . . . . . . . . . . . . . . . 2.3 A coupling between land-surface and atmosphere? . . . . . . . . 2.3.1 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.2 Overview of the main studies on climatology and landatmosphere coupling at a basin scale . . . . . . . . . . . . 2.3.3 Which methodology for the study of land-atmosphere coupling? . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5 5 5 5 6 7 8 8 8 9 10 10 12 14

3 Results 16 3.1 A World overview using ERA40 . . . . . . . . . . . . . . . . . . 16 3.2 How does ERA40 behave in the Murray-Darling Basin? . . . . . . 17 3.2.1 Annual cycles using ERA40 . . . . . . . . . . . . . . . . 17 3.2.2 Time scales of land-atmosphere coupling . . . . . . . . . 20 3.3 Comparison with other re-analysis: . . . . . . . . . . . . . . . . . 20 3.3.1 Surface radiations . . . . . . . . . . . . . . . . . . . . . . 20 3.3.2 Water cycle . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.3.3 Land-atmosphere coupling . . . . . . . . . . . . . . . . . 22 3.3.4 Soil moisture-precipitation feedback: . . . . . . . . . . . 23 3.4 What about Global Circulation Models? . . . . . . . . . . . . . . 25 3.4.1 GCMs description of land-atmosphere coupling in the MurrayDarling Basin . . . . . . . . . . . . . . . . . . . . . . . . 25 3.4.2 Consequences for climate change (HAD model) . . . . . . 26 4 Properties of the land-atmosphere coupling in the Murray-Darling Basin 30 4.1 External influences in the Murray-Darling Basin . . . . . . . . . . 30 4.2 Soil moisture-precipitation cycle in the Murray-Darling Basin using ERA-40 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2

4.2.1 4.2.2 4.2.3

Atmospheric moisture
soil moisture . . . . . . . . . . . Soil moisture
precipitation . . . . . . . . . . . . . . . . Can this analyze enable us to conclude on one mechanism for the Murray-Darling Basin . . . . . . . . . . . . . . .

31 32 34

5 Discussion 35 5.1 Accuracy and physical consistency of Reanalysis in the MurrayDarling Basin . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 5.1.1 Water and Energy Budget . . . . . . . . . . . . . . . . . 35 5.1.2 Soil moisture nudges . . . . . . . . . . . . . . . . . . . . 36 5.2 Need for direct observations of soil parameters in the MurrayDarling Basin . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 5.3 Land-atmosphere coupling: Need to improve GCMs? . . . . . . . 37 5.4 What can be done to go further in the understanding of landatmosphere coupling? . . . . . . . . . . . . . . . . . . . . . . . . 37 6 Conclusion

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1 Introduction Interactions between land and atmosphere occur at different time scales, are not spatially uniform, and concern energy variables as well as moisture variables. Moreover these interactions are not conserved with spatial scaling. This complexity is the reason why there are a lot of study on these interactions, but just a few at the same temporal and spatial scales than this study on the Murray-Darling Basin. Indeed the study of these interactions, on a period greater than a decade, and at a regional to continental scale, has only been possible since the use of numerical global models. Re-analyses and coupled atmosphere-ocean general circulation models(CAOGCMs or GCMs) have been playing a large part in the understanding of land-atmosphere coupling by providing a spatio-temporal regular database for the entire world. Some studies on land atmosphere interactions were achieved quite recently on some of the major basins of the world like the Mississippi Basin [Roads et al., 2002] or the Amazon Basin [Betts and Viterbo, 2005, Betts et al., 2005]. The Murray-Darling Basin (MDB) is a basin that is analysed because of its particularities: it is a semi-arid area with a high spatial range of climatological conditions and with a high inter and intra annual variability; but above also because of the importance of the MDB in Australia’s society: on one hand it is the Australia’s wheat belt and main water reserve, and on this other hand it suffers from many environmental problems linked to its climatology and to anthropogenic activities. This is why this study has been achieved. Analyzing and determining the strength of the land-atmosphere coupling in the MDB is a key element in the prospect of improving GCMs. GCMs are the best existing tools to foresee and anticipate climate change. Which is vital for the MDB and Australia. However assessing the strength of land-atmosphere coupling is not trivial because of the complexity of the mechanisms involved. A statistical approach does not enable the assessment of causality links, but enables the assessment of the co-evolution between two variables. The purposes of this study are to analyze the properties of the land-atmosphere coupling with a statistical approach based on ERA-40 re-analysis; to highlight the impact of the integration time step on the statistical links between land and atmosphere; and to determine the effect of climate change on the strength of the land atmosphere coupling.

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2 Presentation, state of the art and methodology 2.1 The Murray-Darling Basin 2.1.1 Geographical presentation The MDB is located in the south-east of Australia and spreads over 5 states, New South Wales, A.C.T., Victoria, Queensland, and South Australia (Fig2). It covers 1, 061, 469 km2 , which represents 14% of Australia. The Basin is organized around the Murray river, in the south-east, the Darling river, in the north, and their tributaries. The length of the Murray river is 2, 575 km , while its main tributary, the Darling river, is 2, 739 km long. The Murray-Darling river system is the largest of Australia. It is also one of the world’s principal river systems: 15th longest river of the world; 21th in terms of area. The relief extends from sea level in the southwest, with a large area below 200 m in the central plain, to more than 1000 m, in the south-east and Figure 2: Geographical east border of the basin with Mt Kosciuszko risand political map of easting to 2228 m. ern Australia and of the MDB 2.1.2 Climate and natural environments

[http://en.wikipedia.org/wiki/Murray Darling, ]

The MDB is considered to be a semi-arid region, although some of its eastern parts receive more than 1000 mm.year−1 . More than three quarter of this basin receives less than 600 mm.year−1 . (Fig3) This spatial variabilty from the wet east to the dry west consequently has a huge diversity of natural environments: rainforests, subtropical areas, semi-arid and arid lands”[Prasad and Khan, 2002]. Climate of eastern Australia is strongly correlated to the large climatic mode of variabilty affecting the Pacific: El Nino Southern Oscillation (ENSO). The intra-annual and inter-annual variability is an important particularity of the MDB. Rainfall is maximum in summer and minimum in winter, while soil moisture is maximum in winter and minimum in summer. Even this basic description is variable from year to year (Fig4).

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Figure 3:

Map of the mean rainfall distribution in the Murray-Darling Basin [Prasad and Khan, 2002]

Figure 4: Boxplot of the annual evolution of ERA-40 soil moisture in the MDB. Monthly values are the average of monthly means on the period. 1979-2001. The limits represent from the top to the bottom: 95%, 75%, 50%, 25%, and 5% of dats

2.1.3 Economic activities linked with climat and hydrology The MDB is the heart of Australia’s Agriculture not only because of its large range of climatic conditions which enables a large diversity of plantation, but also 6

because of: its large flat plains; its proximity to the main cities of Australia; and the historical colonisation and development of Australia. Some key statistics [Prasad and Khan, 2002]: • More than 2 million people; • 75% of Australia’s irrigation; • 50% of Australia’s sheep flock, 25% of Australia’s cattle herd, 50% of Australia’s crop land; • Agricultural produce AU$ 10 billion (> 40% of national agricultural produce); • Manufacturing AU$ 10 billion (70% based on agriculture); • Tourism AU$ 3.44 billion. 2.1.4 Environmental and Hydrological issues One particularity of the Murray-Darling river system is that it has a water flow which decreases downstream [http://www.mdbc.gov.au, ]. This is not only due to the very high potential evapotranspiration which exists in this basin, but also because of the use of water for irrigation, storage, and for domestic use. It is considered that ”the mean annual outflow from the Basin to the sea is only 27% of the outflow under natural conditions” [http://www.mdbc.gov.au, ]. It results that despite the fact that it is one of the principal river systems in the world, the Murray-Darling has one of the smallest surface runoff (Table1). River System Length(km)Catchment(km2 )Mean Discharge(M L.sec−1 ) Murray-Darling, Australia 3,780 1,060,000 0.4 Nelson, North America 2,575 1,720,000 2.0 Indus, Asia 2,900 1,166,000 5.0 Danube, Europe 2,850 816,000 7.0 Ganges-Brahmaputra, Asia 2,897 1,621,000 38.0 Zambesi, Africa 3,500 1,330,000 7.0 Tocantins, South America 2,699 906,000 10.0 Tigris-Euphrates, Middle East 2,800 1,114,000 1.0 Table 1: Presentation of the main features of the MDB and of 7 other basins which catchment size is equivalent to the size of the MDB [Britanica, ]

An other aspect of the Murray-Darling system is the high inter-annual variability of hydrological conditions which leads to a high variability of the outflow 7

discharge. Over the period 1894-1993, the annual discharge at the mouth of the Murray river has ranged from 1, 626 GL to 54, 168 GL [Maheshwari, 1995]. Last but not least the different natural environments of the Murray-Darling Basin are a shelter for many species: 85 mammals, 367 birds, 151 reptiles, 24 frogs and 20 freshwater fish [http://www.mdbc.gov.au, ]. Some of them are endangered species: 35 birds, 16 mammals (20 mammals species are already extinct).

2.2 Available Database Three kinds of data are available for studying the past climat: • Direct observational; • Output from re-analysis; • Output from models, and more generally from coupled atmosphere-ocean general circulation models (AOGCMs or GCMs). 2.2.1 Observations: A complete atmosphere and land-surface description extracted from observations is not possible in the MDB. Despite the fact that a satisfactory net of meteorological stations exist in the MDB, the number and distribution of soil moisture stations are not sufficient. 2.2.2 Outputs from re-analysis: A re-analysis is a computation of past weather on a regular grid, using finite and irregularly distributed observations from the past, by an up-to-date numerical weather prediction (NWP) model. GCMs are used to generate re-analyses forced by observations. The observations are fed into the model at each temporal step. The output is a complete state of the past climate, including many derived fields (soil moisture, ...), for each temporal step and for each cell of the homogeneous world 3D spatial grid. The two main differences with a simple analysis are that a re-analysis keeps using the same NWP model, and that a re-analysis is not done in real time. We have been looking at three different re-analyses (See Appendice 1 for further details): • The latest reanalysis from the European Centre for Medium-Range Weather Forecasts (ECMWF) called ERA-40;

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• The reanalysis from the National Centers for Environmental Prediction (NCEP) and from the National Center for Atmospheric Research (NCAR) called NCEP/NCAR Reanalysis Project or NCEP R1; • Another reanalysis from the National Centers for Environmental Prediction (NCEP) and from the Department of Energy (DOE) called NCEP/DOE AMIP-II Reanalysis or NCEP R2. The reason why we have been looking at three re-analyses instead of focusing only on one re-analysis, is mainly explained by the problem encountered concerning the physical consistency of each re-analysis. This point will be discussed further. The temporal range of our study goes from 1979 to 2001 and is included in the satellital period, which enables us to eliminate some uncertainties concerning the quality of the observations used in re-analyses. 2.2.3 Outputs from CAOGCms: A GCM is a time-dependent numerical model of the atmosphere. The main difference with re-analysis is that the evolution of the state of the atmosphere in a GCM depend only on the initial inputs and on the physical laws used. The governing equations are the conservation laws of physics. These equations are integrated using the initial conditions. We have been using the outputs of three different CAOGCMs, which have contributed to the Intergovernmental Panel on Climate Change (IPCC): • The GFDL-CM-2-0 model from the Geophysical Fluid Dynamics Laboratory; • The Had-CM-3 model from the Hadley Centre; • The IPSL-CM-4 model from the Institut Pierre-Simon Laplace, the Laboratoire de Meteorologie Dynamique, and the Laboratoire des Sciences du Climat et de l’Environnement. The scenarios used are: • The climate of the 20th Century experiment (20C3M) which goes from 1859 to present. Its initial condition is a pre-industrial climat state It is forced by anthropogenic and natural perturbations. • SRESA2 which goes from present to 2100. Its initial condition is the climate of the end of the 20C3M run. It is based on the estimation of future emissions of greenhouse gazes. 9

The data from IPCC models are archived at the Web site of the PCMDI Program for Climate Model Diagnosis and Intercomparison [http://www pcmdi.llnl.gov/, ].

2.3 A coupling between land-surface and atmosphere? 2.3.1 Theory A short introduction to land-atmosphere interactions: In atmospheric sciences the common former vision of the interaction between land-surface and atmosphere was most of the time reduced to the actions of atmosphere on surface. Nevertheless views have recently changed. Nowadays the acknowledgment of the major roles played by soil parametres on atmosphere are taken into account in most of the studies. Two types of coupling exist between land and atmosphere: • The energy coupling, which includes the exchanges between radiative fluxes and heat fluxes; • The water balance, which includes the exchanges between soil water and atmospheric water for all phase. Obviously these two different couplings are linked and inter-dependent: • Energy transport induces water instability, and so water transport; • Water transport induces energy transport, via rainfall, latent heat flux or ground heat flux. Physics of land-atmosphere interactions: We are considering here a simple, horizontal, theorical, two dimensional model (2D) [Roads et al., 2002, modified]. • Conservation of water in 2D: The two state variables for these water mass conservation equations are P W the vertical integrated precipitable water, and SM the vertical integrated soil moisture, for each water phase. – Atmospheric water:

– Soil water:

∂P W = E − P − WC ∂t

(1)

∂SM = P − E − WR ∂t

(2)

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Where P is precipitation, E is evaporation, W R is continental water transport or water runoff, and W C is atmospherical water transport or water convergence.

• Conservation of energy in 2D: The two states variable for these two temperature equations are Ta the air temperature, and Ts the soil temperature. – Atmospheric energy: Cp

∂Ta = RNa + SH + EW CP + HC ∂t

(3)

We have neglected kinetic energy in first approximation.

– Surface energy: Cv

∂Ts = RNs − SH − λE − G ∂t

(4)

Where RNs and RNa are the net radiation respectively at the surface and at the atmospheric layer considered, SH is the sensible heat flux from the surface, EW CP is the energy variation due to water phase changes, HC is the heat convergence other than SH, λE is the latent heat flux from the surface, and G the ground heat flux from the surface.

• Surface energy partition in 2D: The surface receives its energy from solar and downward longwave radiations. This amount of energy, i.e. net radiation, is balanced by the out-coming sensible, latent and ground heat flux. The partition between sensible heat flux, which is purely a heating transfer, and latent heat flux, which also includes water transport, is called the Bowen ratio. – Surface net radiation: RNs = S ↓ (1 − αs ) + L ↓ −L ↑

(5)

Where S ↓ is the surface shortwave downward flux, L ↓ is the surface longwave downward flux, L ↑= σTs4 is the surface longwave upward flux, and σ is the Stefan-Boltzman constant.

– Bowen ratio: H B= = λE

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r ρcp Tsr−T a

ρcp γ

³

e∗ (Ts )−er rs +ra

´

(6)

Where ρ is air density, cp is the specific heat of air, γ is psychometric constant, ra is aerodynamic resistance, rs is the surface resistance to the transfer of water from the surface to the air, Tr is a reference temperature above the surface, e∗ (Ts ) is the saturated vapor pressure at the surface temperature, and er is the vapor pressure at the reference height.

This theoretical 2D model does not provide a complete solution to the understanding of complex land-surface atmosphere interactions, but it gives a first description of the main mechanisms driving these interactions. An example of interaction: the rainfall soil moisture feedback One of the most conceivable feedback mechanisms is the one between soil moisture and rainfall [Elfatih and Eltahir, 1998] (Fig5). An increasing of surface soil moisture tends to increase the surface absorption of solar radiation, and so to decrease surface albedo, and to increase surface net radiation. An increasing of soil moisture also provides more available water for evaporation, and has for consequence a decreasing of the Bowen Ratio. The results of these two trends are the increase of heat and water fluxes from the surface to the boundary layer. The direct consequence is an increase of moist static energy (mse) near the surface, and an increase of the moist static energy gradient in the boundary layer. Moist static energy includes potential energy, sensible heat and latent heat (7): mse = gz + Cp T + Lq

(7)

Where g is gravitational acceleration, z is elevation, Cp is the specific heat capacity at constant pressure, T is temperature, L is latent heat of vaporization, and q is water vapor mixing ratio.

The last steps of this feedback are: the strengthening of large scale circulation due to the strengthening of moist static energy gradient; And also an increasing of the frequency of convective storms. These phenomena induce more precipitation. So the result of an increasing of soil moisture is an increasing of rainfall. However this theoretical feedback is not physically consistent at regional scale, as only a small fraction of water evaporated from an area returns to the landsurface as a precipitation in this area [Trenberth, 1998] 2.3.2 Overview of the main studies on climatology and land-atmosphere coupling at a basin scale The study of land-surface and atmosphere interactions can be made at a large range of scale:

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Figure 5: Presentation of one hypothesis for relating soil moisture conditions and subsequent rainfalls[Elfatih and Eltahir, 1998]

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• The local scale: based on data from direct observations which enables an accurate study of physical processes. However conclusions on surfaceatmosphere interactions at this scale are strongly dependent on surface parametrisation, land cover, and vegetation type [Small and Kurc, 2003]. • The global scale: based on data from re-analysis or GCMs only, which enables the quantification of the strength of the coupling between land and atmosphere for each model [Guo et al., 2005] and to draw some general conclusions, although these conclusions are models dependent. • the regional-continental scale: this scale, which is the scale of the MDB, can be studied with global models and also with direct observations in some areas. The Global Energy and Water Cycle Experiment (GEWEX), which aims to improve the simulation of water and energy exchange processes in global climate and weather models, has driven a great number of regional-continental studies. The main thematics are water budget, energy budget, and hydrometeorology of GCMs or re-analysis. Three of the major basins have been analysed in detail: • Mackenzie River Basin [Betts and Viterbo, 2000, Betts et al., 2003]. • Mississippi River Basin [Roads and Betts, 2000, Roads et al., 2002](ref ERA 17); • Amazon Basin [Betts et al., 2005, Betts and Viterbo, 2005]. All these studies are based on a comparison of annual time series, and do not precisely describe the links between atmosphere variables and land-surface variables. 2.3.3 Which methodology for the study of land-atmosphere coupling? A. Betts’ methodology: example of the Madeira Basin using ERA40 Some more recent studies have found a more accurate way to describe the links between surface and atmosphere variables. Betts, in 2004 and then in 2005, [Betts, 2004, Betts and Viterbo, 2005] has proposed to analyse data from models by plotting some atmosphere variables, like net radiation, relative humidity, sensible and latent heat flux, in function of soil variable, like soil moisture and temperature . By looking at annual cycle, A. Betts can comment the strength of the correlation between these two types of variable. The value of the correlation gives no real information on some possible links of causality, but it enables him to forecast the co-evolution of an atmosphere parameter and of a land-surface parametre. 14

A. Betts and P. Viterbo have undertaken this kind of study for the Madeira Basin, a southwestern basin of the Amazon [Betts and Viterbo, 2005]. They have found some tight coupling, for mean annual cycle, between soil moisture or water index SM I and relative humidity RH or pressure of lifting condensation level PLCL (see Appendice 2 for Fig23 and for definitions). Note that PLCL pressure of lifting condensation level is in fact on this figure the difference of pressure between the surface and the lifting condensation level; we will keep this convention in this study. Such a tight coupling is remarkable. Some other results, between other variables like SM I and total cloud cover T CC, do not show a strong coupling or even no coupling at all. Nevertheless these kinds of links enable to describe the coupling between land-surface and atmosphere: • Which variable of atmosphere and land-surface are part of this coupling; • What is the strength of these interactions; No conclusions can be expressed concerning causality links directly from these results. Moreover the validity of these results depend on the quality of the reanalysis used, here ERA40. Next steps How is it possible to go further in the description of the coupling between land-surface and atmosphere? • By doing this study for all the major basins; • By comparing re-analysis with direct observations to ensure the validity of the results; And if no real net of data exists in the area, comparing different re-analysis. Another issue linked with the coupling between land-surface and atmosphere, is the validation of GCMs. This validation is necessary to assess climate change, which is environmentally and economically important. The Global Land-Atmosphere Coupling Experiment (GLACE) has compared the strength of this coupling for twelve GCMs [Guo et al., 2005]. They have looked at the relations between soil moisture and evaporation, evaporation and precipitation, and preciptation and soil moisture. Two of their conclusions are that the strength of the coupling is widely variable from model to model (See Appendice 3), and spatially variable.

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3 Results 3.1 A World overview using ERA40

Figure 6: Worldwide map of the correlation of the time series of the monthly means of ERA-40 Relative Humidity and Soil Moisture, on the period 1979-2001.

The first comment that can be made on the worldwide map of correlation between soil moisture and relative humidity is that correlation is not uniform. This correlation ranges from almost −0.6 to 1 (Fig6). This highlights the fact that it is difficult to describe the coupling between land-surface and atmosphere at a global scale. The second comment is that the MDB is not very remarkable: • At a continental scale this basin does not seem to behave differently from the Australian mean behaviour. • At a global scale Australia and the MDB appear to have reasonable correlations. Whereas the Amazon and the Gange Basin have the highest correlation which is very close to 1. The third comment is that the correlation between soil moisture and relative humidity is significantly correlated with rainfall at global scale (Fig6, see Appendice Fig24). The hot and cold desert areas like Sahara or Siberia have a correlation between soil moisture and relative humidity close to 0, while wet areas are highly correlated. 16

3.2 How does ERA40 behave in the Murray-Darling Basin? 3.2.1 Annual cycles using ERA40 Soil moisture / relative humidity-pressure of lifting condensation level: We have used the same methodology as A. Betts [Betts, 2004] for analysing the MDB. We have been looking at the coupling between SM I and some atmosphere variables, RH, PLCL (Fig7). These annual cycles are made with monthly means during the period 1979-2001.

Figure 7: Annual cycles of the monthly means values of ERA-40 relative humidity (A) and Pressure of lifting condensation level (B) in function of the monthly values of the soil moisture index in the first layer. Average on the period 1979-2001.

The first comment that can be made is that land-atmosphere interactions in the MDB do not have the same behaviour as the ones in Madeira Basin. The correlation between SM I and RH, or SM I and PLCL , whose values are respectively 0.82 and −0.86 (Table2), are not as strong as in Madeira Basin. It is possible to separate 4 phases, and 2 regimes: • March to June and July to December, where the relation between SM I and RH or PLCL is quasi-linear. An increase of SM I leads to an increase of RH or PLCL and reciprocally. • December to March and June to July , where there is a phase of transition between these two linear behaviour. The relation is also quasi-linear. But an increase of SM I leads to a decrease of RH or PLCL . Soil moisture / precipitation-temperature at 2 metres: Then we have been looking at the coupling between SM I and some other atmosphere parametres: T2m the temperature at 2 m and P the precipitation (Fig8). The link between SM I and P seems to be complex. The correlation is negative and weak −0.44 (Table2). 17

Figure 8: Annual cycles of the monthly means values of ERA-40 2 meters temperature (A) and precipitation (B) in function of the monthly values of the soil moisture index in the first layer. Average on the period 1979-2001.

We will debate further the validity of the SM I-P feedback as seen by Elfatih [Elfatih and Eltahir, 1998]. Nevertheless the negative link between temperature and SM I seems to be verified in the MDB. The value of the correlation is −0.97. The decreasing of SM I from January to March, despite the decreasing of T2m is probably linked with the decreasing of P during the same period. Soil moisture / net radiations-cloud cover: Radiations are an important part of the energy budget of atmosphere and surface. Radiations are mainly composed of two spectrums: • The solar or shortwave spectrum, which is the forcing term, and depends on the position of the sun and on the surface and atmosphere albedo; • The infrared or longwave spectrum depends on the temperature of the ground, on the temperature of the atmosphere, and on the cloud cover and its distribution. Surface longwave net radiation LWN does not change significantly during the year (Fig9), so that the variation of surface net radiation N R is driven by the annual cycle of surface net shortwave radiation SWN . And SWN depends mainly on solar input here, as total cloud cover T T C does not highly vary during the year. Nevertheless clouds vertical distribution is not constant through the cycle: More low clouds LC and less high clouds HC during winter; Less low clouds and more high clouds in summer; While middle clouds M C is almost constant. Soil moisture / surface fluxes-Bowen ratio: The variations of N R and T CC play major parts on the partition of surface heat fluxes. N R is the input of energy 18

Figure 9: Annual cycles of the monthly means values of ERA-40 surface radiations [W.m−2 ] (A) and cloud covers [%] (B) in function of the monthly values of the soil moisture index in the first layer. Average on the period 1979-2001.

at the surface, whereas T CC and clouds vertical distribution control the input of water at the surface via precipitation. We have compared the annual cycles of latent heat flux LH and sensible heat flux SH, and their ratio, the Bowen Ratio BR (Fig10). The range of SH annual variations is larger than the one of LH.

Figure 10: Annual cycles of the monthly means values of ERA-40 surface heat fluxes [W.m−2 ] (A) and Bowen Ratio (B) in function of the monthly values of the soil moisture index in the first layer. Average on the period 1979-2001.

It can be understood as SH depends on the difference of temperature between the surface and the above atmosphere compared to LH, which depends on the difference of vapor pressure. In summer SH is higher than LH as the soil is dry and temperature is maximum, whereas LH is higher than SH in winter as the soil is wet and temperature is minimum.

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3.2.2 Time scales of land-atmosphere coupling The last section was a description of the interactions between land and atmosphere using monthly means on twenty years. But the coupling between land and atmosphere exists at different time scales. That is why we have compared the values of correlations between variables at different time scales (Table2) The difference between 4∗ monthly means time series and monthly means averaged on the period 1979-2001 are huge for most of the variables. These differences are due not only to the averaging on 20 years but also to the variability of response time. Some variables, like the surface albedo α and SM I are strongly correlated at a monthly time scale and are not correlated at 6 hr time scale. Some others , like LWN , SWN , or T2m respond at both 6 hr and monthly time scales. Comparing correlation for different time scales, and betwwen means values and time series, enables the prevention of some errors of interpretation of the physics of land-atmosphere coupling. For example, on seasonal or monthly scales P and SM I are negatively correlated, although they are positively correlated at 6 hr time scale. The strength of the coupling between SM I and PLCL or RH is approximatively the same at different time scale. The same thing happens for SM I and LC or M C but not for HC. The coupling between SM I and T2m is weaker at 6 hr than at monthly time scale. However the couplings between SM I and net radiations SWN , LWN or N R change radically between monthly and 6 hr time scale, as they are not correlated at 6 hr. Same behaviour for the coupling between SM I and surface heat fluxes SH or LH.

3.3 Comparison with other re-analysis: We have been looking at two other reanalysis, NCEP R1 and R2, so as to compare ERA-40 climatology. In absence of complete surface observations, each re-analysis is a possible climatology. 3.3.1 Surface radiations The range of the maximum difference between these three re-analyses goes from almost 0 to 15 W.m−2 , for both LWN and SWN (Fig11). The shift between NCEP R1 and NCEP R2 is close to constant through the months for LWN and SWN . With NCEP R1 having both the highest SWN and LWN values. The temporal evolution of these re-analyses is quite similar. However a kind of uncertainty remains concerning the values of radiations and especially LWN : the ratio, of the maximum difference between re-analysis to the mean of the three re-analyses for

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Table 2: Chart of the correlation between the main climatological variables of atmosphere

and land-surface for ERA-40. In red the correlation for the mean annual cycle i.e. one averaged value per month. In blue the correlation for the time series with 4 values per month 0, 6, 12 and 18 hr. Both correlations are achieved on the period 1979-2001.

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RH SM I T2m LH SH LWN T CC SWN LC M C HC PLCL N R P BRi α RH 0.74 -0.76 -0.09 0.04 -0.35 0.65 0.05 0.84 0.40 0.10 -0.98 0.10 0.40 0.05 0.09 RH SM I 0.82 -0.56 0.01 -0.18 -0.40 0.62 -0.14 0.76 0.50 0.12 -0.74 -0.11 0.54 0.02 0.05 SM I T2m -0.87 -0.97 0.16 0.13 0.37 -0.24 0.12 -0.73 -0.03 0.26 0.79 0.09 -0.00 -0.06 0.05 T2m LH -0.96 -0.78 0.88 0.92 0.79 -0.29 0.95 -0.23 0.61 0.17 0.15 0.95 0.34 -0.02 -0.42 LH SH -0.96 -0.89 0.95 0.98 0.87 -0.16 0.99 -0.31 0.47 0.09 -0.09 0.99 0.15 -0.02 -0.40 SH LWN -0.99 -0.81 0.86 0.96 0.96 -0.17 0.87 -0.61 0.26 -0.07 0.28 0.84 -0.13 0.00 -0.40 LWN T CC 0.70 0.53 -0.49 -0.50 -0.55 -0.68 0.18 0.59 0.75 0.71 -0.62 0.21 0.65 0.01 0.12 T CC SWN -0.98 -0.83 0.91 0.99 0.99 0.98 -0.57 -0.29 0.50 0.09 -0.11 1.00 0.18 0.02 0.43 SWN LC 0.97 0.89 -0.91 -0.91 -0.91 -0.96 0.72 -0.94 0.20 0.07 -0.80 -0.25 0.35 0.06 -0.06 LC M C 0.08 0.51 -0.38 0.00 -0.18 -0.08 0.28 -0.09 0.20 0.37 -0.41 0.51 0.61 -0.01 0.27 M C HC -0.27 -0.47 0.54 0.44 0.45 0.27 0.44 0.40 -0.28 -0.09 -0.06 0.10 0.51 -0.04 -0.01 HC PLCL -0.99 -0.86 0.91 0.97 0.98 0.99 -0.65 0.99 -0.97 -0.13 -0.06 -0.15 -0.36 -0.05 -0.07 PLCL N R -0.97 -0.83 0.92 0.99 0.99 0.97 -0.55 1.00 -0.94 -0.09 0.42 0.99 0.21 0.02 0.43 N R P -0.55 -0.44 0.61 0.73 0.67 0.56 0.06 0.68 -0.49 0.21 0.66 0.59 0.69 0.01 0.12 P BRi 0.94 0.90 -0.89 -0.85 -0.90 -0.92 0.70 -0.89 0.99 0.23 -0.30 -0.94 -0.88 -0.43 0.01 BRi α 0.99 0.84 -0.89 -0.95 -0.96 -0.97 0.69 -0.97 0.99 0.10 -0.29 -0.98 -0.96 -0.55 0.96 α RH SM I T2m LH SH LWN T CC SWN LC M C HC PLCL N R P BRi α

Figure 11: Monthly means values of ERA-40, NCEP R1 and NCEP R2 shortwave (A) and longwave (B) radiations [W.m−2 ]. Average on the period 1979-2001. N )max ≈ 20%. This value can be the same month, for LWN is not negligible (∆LW meanLWN understood as the maximum uncertainty between these three re-analyses.

3.3.2 Water cycle The differences between re-analysis are more important for the water variable than for the surface radiations. Adimensional soil moisture ASM which is in fact the SM I ratio of the monthly values to the annual mean ASM = meanSM , shows two I kinds of behaviour(Fig12 A): NCEP R2 and ERA-40 which have one maximum in winter and one minimum in summer; NCEP R1 which has one additional maximum in March. It results that the uncertainty concerning each re-analysis is high. The reason why we have analysed ASM instead of SM I is due to the difference of number and height of soil layers between each re-analysis. The behaviour of RH for each re-analysis is quite identical(Fig12 B). NCEP R1 and R2 are very close, whereas ERA-40 RH is higher than the two last ones. The maximum uncertainty is close to 12%. LH and P show a high variability between re-analysis. The maximum uncertainties are respectively 50% and 55%. 3.3.3 Land-atmosphere coupling The comparison of temporal co-evolution of two parameters of the same re-analysis, like RH in function of SM I, is another way of analysing the validity of each reanalysis. So we have been looking at the co-behaviour of the main climatological parametres for each re-analysis (Fig13). The first general comment is that NCEP NCAR or NCEP R1 globally behaves differently from ERA-40 and NCEP R2. These last two ones show some similar

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Figure 12: Monthly means values of ERA-40, NCEP R1 and NCEP R2 Adimensional soil moisture (A), relative humidity [%] (B), latent (C) and sensible (D) heat fluxes [W.m−2 ] . Average on the period 1979-2001.

annual cycle for each parametre, apart from P . This main difference can be understood by the annual cycle of soil moisture which has two maximums for NCEP R1 unlike ERA-40 or NCEP R2. NCEP R2 and ERA-40 are quite similar concerning not only the values of each parametres, but also the coupling between ASM and other parametres. The last comment is that the coupling between ASM and P is weak, and very different between each re-analysis. As NCEP R2 is a new version of NCEP R1, we may formulate the hypothesis that the behaviour of NCEP R2 is better than the behaviour of NCEP R1. So we may assume that NCEP R2 or ERA-40, which are quite similar in the MDB, are the re-analysis references. 3.3.4 Soil moisture-precipitation feedback: An other way to see the soil moisture-precipitation feedback is to look at the transfers of water between land and atmosphere, and how each flux influence each 23

Figure 13: Annual cycles of the monthly means values of ERA-40, NCEP R1 and NCEP R2 relative humidity [%] (A), surface net radiation [W.m−2 ] (B), 2 meters temperature [K] (C), and rainfall [mm.month−1 ] (D) in function of the monthly values of the adimensional soil moisture. Average on the period 1979-2001.

other one. Soil moisture influences surface evaporation or latent heat flux, which influences rainfall, which influences soil moisture (Fig14). The links between SM I and LH or P and SM I are weak, whereas the link between LH and P is strong, and almost linear for the three re-analyses. Moreover the link between SM I and P is negative for the three re-analyses. If we compare that with the values of the correlation between the same variables at 6 hr time scale (Table2), the description of SM I-P feedback is not the same. First of all the link between P and SM I is positive (0.54). Then the correlation between LH and P is weaker (0.34). And SM I and LH are completely non-correlated (0.01).

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Figure 14: The three main steps of the soil moisture-precipitation feedback for ERA-40, NCEP R1 and NCEP: Latent heat flux [W.m−2 ] in function of adimensional soil moisture (A); Rainfall [mm.month−1 ] in function of latent heat flux [W.m−2 ] (B); Adimensional soil moisture in function of Rainfall [mm.month−1 ] (C). Average on the period 19792001.

3.4 What about Global Circulation Models? 3.4.1 GCMs description of land-atmosphere coupling in the Murray-Darling Basin We are now comparing ERA-40 re-analysis with three GCMs, with the same method used for comparing re-analysis between each others (Fig15). GFDL model has a different annual cycle of soil moisture. Compared to ERA40 ASM is anomaly high during winter and at the beginning of spring. It results that this model does not fit the ERA-40 re-analysis. Compare to the two other GCMs, HAD model is the one which is the closest to ERA-40: for the strength of the coupling between soil moisture and atmosphere variables; and for the description of the climatology of the MDB. There is also a soil moisture positive anomaly in winter. IPSL model has the largest annual cycles of this panel of three models. It re25

Figure 15: Annual cycles of the monthly means values of ERA-40, GFDL, HAD and IPSL relative humidity [%] (A), surface net radiation [W.m−2 ] (B), 2 meters temperature [K] (C), and rainfall [mm.month−1 ] (D) in function of the monthly values of the adimensional soil moisture. Average on the period 1979-2001.

sults that the strength of the links between atmosphere variables and soil moisture are weaker. There is no soil moisture anomaly in winter. 3.4.2 Consequences for climate change (HAD model) There are many reasons why we have been studying the co-evolution of land and atmosphere parametres during the 21th century : • It simply gives another approach of climate change; • It enable the comparison of GCMs. In order to estimate climate change and its impact on the MDB, we have focused our studies on three periods of twenty years each: 1979-1999, 2029-2049, and 2079-2099.

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We are going to base our estimation of climate change on the HAD model as it appears to be the one which have the closest climatology with ERA40, compared to the IPSL or GFDL models. Estimation of climate change N R does not change significantly (Fig16). Mean T2m approximatively increases of 3◦ C in 100 years, while RH decreases of 5 %. P evolution is not monotonous on 100 years: there is an increase of summer rainfall and a decrease of winter rainfall from the first period (1979-1999) to the second one (2029-2049); but there is an annual global decrease of rainfall from the first period or the second one to the third one (2079-2099).

Figure 16: Evolution of the annual cycles of the monthly means values of HAD relative humidity [%] (A), surface net radiation [W.m−2 ] (B), 2 meters temperature [K] (C), and rainfall [mm.month−1 ] (D) in function of the monthly values of the adimensional soil moisture. Averages on the periods 1979-2001, 2029-2049, and 2079-2099.

Evolution of land-atmosphere coupling It is hard to determine real trends concerning the consequences of climate change on the strength of the couplings between land and atmosphere (Fig16). The range of climate variations are too small 27

to change radically the co-behaviours of surface and atmosphere variables. So there is no real change of the strength of land-atmosphere coupling. But the atmosphere is getting dryer and dryer through the 10 years, as LH RH or P are decreasing. Meanwhile there is no real change of soil moisture in the HAD model. So it results that there is a transfer in the 2D space of atmosphere vs land-surface from an initial state to a dryer atmosphere state.

Figure 17: Evolution of the three main steps of the soil moisture-precipitation feedback for HAD: Latent heat flux [W.m−2 ] in function of adimensional soil moisture (A); Rainfall [mm.month−1 ] in function of latent heat flux [W.m−2 ] (B); Adimensional soil moisture in function of Rainfall [mm.month−1 ] (C). Averages on the period 1979-2001, 2029-2049, and 2079-2099.

Future evolution of the soil moisture-precipitation feedback As for the reanalysis, the coupling between LH and P is the strongest of the cycle (Fig17). The two other interactions are complex with no linear relations between SM I and LH or P and SM I. It is not possible, thanks to this graph (Fig17), to conclude on the evolution of the soil moisture-precipitation feedback.

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Comparison with the IPSL and GFDL models The climatological evolutions of energy or temperature variables of the IPSL or GFDL models are quite comparable to the evolutions of the HAD model (see Appendice 5 Fig??): N R does not change and T2m decreases of 3◦ C. However there are some differences: • IPSL: RH does not change for whole the year, apart for winter where there is a slight increase with time. The evolution of P has to be separated in two phases: a monotonous high decrease in autumn through 100 years, and a non-monotonous decrease in spring with a small increase from the first period to the second one. Winter and summer rainfall temporal trend is slightly decreasing. • GFDL: RH radically decreases (6 %) from the first period to the second one, whereas there is a slight increase from the second to the third period. P globally decreases, and the autumn maximum of the first stage does not exist in the second and third stage.

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4 Properties of the land-atmosphere coupling in the Murray-Darling Basin 4.1 External influences in the Murray-Darling Basin

Figure 18: Average distributions of precipitation in Australia for January, April, Jully and October. Average on the period 1961-1990. From the Bureau of Meteorology research Centre.

The MDB is a semi-arid area. Compared to the Amazon Basin, their is a huge lack of water. It results that SH is higher than LH, and that BR is most of the time greater than 1. A consequence is that the transfers of water between atmosphere and land are less than the transfers in the Amazon Basin. It results that the hydroclimatology of the MDB is more sensitive to external influences, and that a larger part of its climatology has an external origin. So the interactions between land and 30

atmosphere in the MDB are strongly dependent on the atmosphere inputs coming from external areas. Spatial distribution of rainfall in the MDB is very dependent on external conditions. In Australia most of the precipitation occurs in the north in Summer and in the south in Winter (Fig18). Spring and Autumn are the transition states between these two extremal conditions. It results that the MDB is strongly influenced by external processes and by their seasonal variations.

4.2 Soil moisture-precipitation cycle in the Murray-Darling Basin using ERA-40 During this study we have been looking only at the co-behaviour of atmospheric and land variables. In any case we have described some causal links between these variables even if they could be established by having a logical approach of the physical mechanisms. As we have shown (Table2) the links between variables can change depending on the integration time of the variables. It is important to understand that the mechanisms which link the atmosphere to the land can be the same at different time scales even if the links between variables are not the same. Another remark is that we are not studying an autonomous and independent basin, rather a basin which is under the influence of different forcings: • Radiation forcing, which does not have the same effect at a 6 step and at a monthly step; • Meteorological forcing from external events. It results that some internal mechanisms may be hidden by external forcings. 4.2.1 Atmospheric moisture
soil moisture At monthly time step with averaged data on 20 years There is no positive correlation between RH and P (−0.55) with a time step of one month (Table2). That does not mean that an increase of RH induces a decrease of P which is physically not consistent. But that means that the precipitation response time to an increase of RH is more likely to be less than one month. An external influence may also explain a part of this negative correlation. At 6 hr time step for time series The link between atmospheric wetness and soil moisture is quite strong in the MDB (Fig19) at a 6 hr time step. RH is strongly linked to T CC, which is strongly linked to P recipitation. We can assume that RH induces T CC, which induces P . And an increase of P induces 31

Figure 19: Statistical relations linking atmospheric moisture to soil moisture for ERA40. Using correlations of the 4x monthly values calculated previously (Table2).

an increase of SM I despite the high value of potential evapo-transpiration in the MDB But the link between SM I and RH is not obvious, even if the correlation is strong. It will be easy but false to say that SM I controls RH. Land moisture modifies atmospheric moisture mostly via evaporation, and also by surface radiations fluxes and SH. But SM I and LH are not correlated (0.01, Table2). And SM I is poorly correlated to SH and to surface radiations fluxes. So RH is more probably strongly linked to SM I via clouds and precipitation. 4.2.2 Soil moisture
precipitation At montly time step with averaged data on 20 years We are looking at the soil moisture-precipitation feedback as described by Eltahif [Elfatih and Eltahir, 1998]. We compare his description with the description of the Murray-Darling Basin made from ERA40 re-analysis outputs (Fig20). We can focus our comparison on the key element of this mechanism, the link between soil moisture and net radiations. In the Murray-Darling an increase of soil moisture is related with a decrease of net radiations at the surface. This description is the opposite of the soil moisture- precipitation feedback mechanism as seen by Eltahif [Elfatih and Eltahir, 1998] (Table2). That does not mean that this mechanism is incorrect. There are two main differences: • Soil moisture is positively correlated to surface albedo in the Murray-Darling, while an increase of soil moisture leads to a decrease of surface albedo in Eltahif’s mechanism; • Bowen Ratio is positively correlated to net terrestrial radiations in the MurrayDarling, while a decrease of Bowen Ratio leads to an increase of net terrestrial radiations in Elathif’s mechanism. 32

Figure 20: Statistical relations linking soil moisture to net radiations for ERA-40. +: positive correlation; textcolorblue−: negative correlation; textcolorgreen : no correlation. Using correlations of the monthly means calculated previously (Table2).

It results that the link between soil moisture and precipitation is negative (−0.44, Table2).

Figure 21: Statistical relations linking soil moisture to net radiations for ERA-40. +: positive correlation; −: negative correlation; : no correlation. Using correlations of th 4x monthly values calculated previously (Table2).

At 6 hr time step for time series At 6 hr time step, the links are different. There is no correlation between soil moisture and net radiations. This statement seems to depend on the fact that soil moisture is not correlated to surface albedo or Bowen Ratio at this scale of time. Nevertheless soil moisture and precipitation are positively correlated (0.54, Table2).

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4.2.3 Can this analyze enable us to conclude on one mechanism for the Murray-Darling Basin We have illustrated the fact that the sign and the strength of the feedback between soil moisture and precipitation in the Murray-Darling can change depending on time scale. But that does not mean that there are more than one response of precipitation to an increase of soil moisture. What is more conceivable is that the response of precipitation to an increase of soil moisture can not be understood with this methodology and these two scales of time. I assume that a period of one month or 6 hr are respectively too long or too small to fit the signal of the precipitation response. The second hypothesis is that the amplitude of the signal which goes from soil moisture to precipitation is too weak compared to the amplitude of variations due the radiative forcing term. The 6 hr period fits the period of oscillation from diurnal to nocturnal conditions, whereas the period of one month fits the seasonal oscillation of radiations The same problem exists concerning the influence of atmospheric water on SM I. Even if this influence is well understood with a time step of6 hr.

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5 Discussion 5.1 Accuracy and physical consistency of Reanalysis in the MurrayDarling Basin Re-analysis like ERA-40 are the best available present set of data to describe the climatology of the Murray-Darling Basin. Nevertheless re-analysis are not perfect even if the models that are used represent the most recent state of the art. 5.1.1 Water and Energy Budget Energy and water budgets are some key elements of GCMs and re-analysis. The closure or not of these budgets is a condition for assessing on the validity and on the quality of models.

Figure 22: ERA-40 Water (A) and energy (B) budgets for the MDB. Using monthly means on the period 1979-2001. P is precipitation [mm.month−1 ], −E is evaporation [mm.month−1 ], −∆SW is the difference of soil water [mm.month−1 ] between 2 months, W B the water budget is the sum of the three last variables. N R is surface net radiations [W.m−2 ], LH and SH are respectively latent and sensible heat fluxes [W.m−2 ], and EB the energy budget is the sum of the three last variables.

ERA-40 energy budget EB is close to 0 (Fig22). The temporal oscillations of this budget around 0 can be explain by the variations of soil temperature (Equation4). And we have not taken into account the variations of G the ground heat flux which is negligible compare to LH and SH. But ERA-40 water budget W B is not close. The range of W B variations goes from −5 to −22 mm.month1 . We have not taken into account the runoff R, or snow fluxes in W B (Equation2). But runoff and snow fluxes are negligible in the MDB, which is a semi-arid area. So there is definitely a problem of water budget in ERA-40 in the MDB. This problem is probably due to unrealistic values of P and E in the MDB [Hagemann et al., 2005]. On the period 1971-2001 the average P or E are for 35

ERA-40 are not close to observations: PERA40 ≈ 80% and EERA40 ≈ 110%. The Pobs Eobs consequence is a lack of precipitation and an excess of evaporation for ERA-40 in the MDB. 5.1.2 Soil moisture nudges We have realized during this study that re-analysis have to be used with precaution. Moreover for a study which results are dependent on the parameterization of soil moisture. Direct observations for soil moisture are scarce and irregular. So it results that models are not able to correctly describe soil moisture evolution without a correction term. This correction term is called a nudging term. ERA-40: In ERA-40 soil moisture is corrected at each time step (6 hr) by a nudging term [Douville et al., 2000] (Equation9). This nudging is computed from the values of atmospheric specific humidity close to the land-surface. θia = θif + Cv D∆t(q a − q f ) θia

(8)

θif

Where and are the analyzed and first-guess values of the volumetric soil water contents of soil layer i with i = 1, 2, or3; q a and q f are respectively the analyzed and first-guess values of lowest model level specific humidity; Cv is the fraction of vegetation cover; ∆t = 6h; and D = 1.04 is an empirically determined constant.

Soil moisture is dependent on this nudging term. It was introduced in the ERA40 model because free-running soil moisture turns out to drift. So soil moisture distribution and temporal evolutions are not realistic. NCEP R1: There is a nudging term which is used in NCEP R1. This nudging term depends on climatology [Kalnay et al., 1996]. NCEP R2: NCEP R2, which is a new version of NECP R1, used a different correction. The nudging of soil moisture is based on the difference between computed rainfall and observed rainfall on five days (pentad). ”If the model-generated precipitation is greater (less) than the observed precipitation, the difference is substracted from (added to) soil moisture at the topsoil layer during the following pentad” [Kanamitsu et al., 2002]. Another modification occurs depending on the values of runoff.

5.2 Need for direct observations of soil parameters in the MurrayDarling Basin Land-atmosphere interactions are complex. Accuracy is more than needed to understand these interactions. As discussed previously re-analysis suffer from the 36

lack of direct observations of soil moisture. It results that re-analysis soil moisture is not realistic, and that the understanding of land-atmosphere coupling can not be done with accuracy. The Ozflux and OzNet projects are not enough developed and with a too irregular distribution to give a real answer to this lack of data in the MDB. So we need to create some new soil moisture sites and some new surface fluxes stations all around the Murray-Darling Basin. The comprehension of land-atmosphere coupling is very important for assessing climate change in the MDB. And this comprehension is not optional as the MDB, which is the is vital for Australian economy.

5.3 Land-atmosphere coupling: Need to improve GCMs? Another consequence of the imprecision of soil moisture in re-analysis is the difficulty to judge GCMs. A classification of twelve GCMs depending on the strength of land-atmosphere coupling has already been realized [Guo et al., 2005] (See Appendice 3). The next step was to say which strength correspond to the real one. But we have not been able to determine this strength as soil moisture is not reliable in re-analysis. Moreover we have shown in this study that statistical links between land and atmosphere variables are not conserved with a change of time step. It results that the assessment of the strength of land-atmosphere coupling need to be done for different time step as well as for re-analysis as GCMs.

5.4 What can be done to go further in the understanding of land-atmosphere coupling? Statistical links between atmosphere and land variables change with time step. It results that it is difficult to conclude one the strength of the coupling between atmosphere and land. What I suggest is to look at the evolution of the correlation between land variables, as SM I, and atmosphere variables as P , depending on time step (Fig27). This kind of approach will probably enable to understand the variations of strength in the coupling between land and atmosphere with time step. Moreover it will enable to quantify the time scale of each interactions

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6 Conclusion The Murray-Darling Basin climatology is strongly influenced by external forcings. It results that the climatic internal signal coming from the coupling between land and atmosphere is disrupted. Moreover the panel of re-analyses that we have used do not converge on one climatology. By consequence a high uncertainty remains on the consistency of our results. We have shown that the strength of the land-atmosphere coupling is weaker in the Murray-Darling Basin than in Madeira Basin. The statistical links between land and atmosphere change depending on the integration time step. For example the soil moisture-precipitation feedback does not have the same statistical behaviour with a time step of 1 month or with one of 6 hours. This statistical comparison between re-analyses has enable to determine that the HAD-CM-3 global model has a climatology and a land-atmosphere coupling that are similar to ERA-40 in the Murray-Darling Basin. More similar than the IPSL or the GFDL models. Climate change does not radically disrupts soil moistureprecipitation feedback and more generally land-atmosphere interactions in HADCM-3 using SRESA2 scenario.

Acknowledgements I first would like to thank my supervisors: Dr. Bryant McAvaney for his warmhearted welcome, for his help during all the steps of my internship, and above all for having share his general knowledge of climate sciences; Dr. Bertrand Timbal for his kindness and help, and for his careful reviews of this report. I also warmly thank Lawson Hanson for his grateful help and for his valuable advice on programming. I especially acknowledge Prof. Andrew Pitman for our enriching discussions on land-surface scheme. I also acknowledge the Macquarie University for its invitation. Grateful thanks to Caitlin Wilks for her ”fussy and pernickety” review of this report. I acknowledge the OzNet project and more especially Dr. Andrew Western for having kindly provided their observations of the Murrumbidgee Catchment. I also acknowledge the Ozflux project and more precisely Dr. Ray Leuning for having kindly provided their observations of Tumbarumba station. I finally acknowledge the Bureau of Meteorology Research Centre, and more especially the Climate Dynamics team for their warm welcome. Special thanks to my housemates, to my Australian familly, to the Bomeroos, to the Hofts and to all my friends for their support and our enriching conversations and activities. 38

References [Betts, 2004] Betts, A. K. (2004). Understanding hydrometeorology using global models. Bulletin of the American Meteorological Society, 85(11):1673–1688. [Betts et al., 2003] Betts, A. K., Ball, J. H., and Viterbo, P. (2003). Evaluation of the era-40 surface water budget and surface temperature for the mackenzie river basin. Journal of Hydrometeorology, 4(6):1194–1211. [Betts et al., 2005] Betts, A. K., Ball, J. H., Viterbo, P., Aiguo, D., and Marengo, J. (2005). Hydrometeorology of the amazon in era-40. Journal of Hydrometeorology, 6(5):764–774. [Betts and Viterbo, 2000] Betts, A. K. and Viterbo, P. (2000). Hydrological budgets and surface energy balance of seven subbasins of the mackenzie river from the ecmwf model. Journal of Hydrometeorology, 1(1):47–60. [Betts and Viterbo, 2005] Betts, A. K. and Viterbo, P. (2005). Land-surface, boundary layer, and cloud field coupling over the southwestern amazon in era40. Journal of Geophysical Research, 110. [Britanica, ] Britanica, E. Volume 26, 846. [Douville et al., 2000] Douville, H., Viterbo, P., Mahfouf, J.-F., and Beijaars, A. C. M. (2000). Evaluation of the optimum interpolation and nudging techniques for soil moisture analysis using fife data. Monthly Weather Review, 128. [Elfatih and Eltahir, 1998] Elfatih, A. and Eltahir, B. (1998). A soil moisturerainfall feedback mechanism. Water Resources Research, 34(4):765–776. [Guo et al., 2005] Guo, Z., Dirmeyer, P. A., Koster, R. D., Bonan, G., Chan, E., Cox, P., Gordon, C. T., Kanae, S., Kowalczyk, E., Lawrence, D., Ping, L., Lu, C.-H., Malyshev, S., McAvaney, B., McGregor, J. L., Mitchell, K., Mocko, D., Oki, T., Oleson, K. W., Pitman, A., Sud, Y. C., Taylor, C. M., Verseghy, D., Vasic, R., Xue, Y., and Yamada, T. (2005). Glace: The global land-atmosphere coupling experiment. Journal of Hydrometeorology. submitted on February 11, 2005. [Hagemann et al., 2005] Hagemann, S., Arpe, K., and Bengtsson, L. (2005). The era-40 archive. Validation of the hydrological cycle of ERA-40, 24. [http://data.ecmwf.int, ] http://data.ecmwf.int. Ecmwf. [http://en.wikipedia.org/wiki/Murray Darling, ] http://en.wikipedia.org/wiki/Murray Darling. Wikipedia. 39

[http://www pcmdi.llnl.gov/, ] http://www pcmdi.llnl.gov/. Pcmdi. [http://www.cdc.noaa.gov, ] http://www.cdc.noaa.gov. Noaa. [http://www.mdbc.gov.au, ] http://www.mdbc.gov.au. Mdbc. [Kallberg et al., 2004] Kallberg, P., Simmons, A., Uppala, S., and Fuentes, M. (2004). The era-40 archive. ECMWF ERA-40 Project Report Series, 17. [Kalnay et al., 1996] Kalnay, E., Kanamitsu, M., Kistler, R., Collins, W., Deaven, D., Gandin, L., Iredell, M., Saha, S., White, G., Woolen, J., Zhu, Y., Leetmaa, A., Reynolds, B., Chelliah, M., Ebisuzaki, W., Higgins, W., Janowiak, J., Mo, K. C., Ropelewski, C., Wang, J., Jenne, R., and Joseph, D. (1996). The ncep/ncar 40-year reanalysis project. Bulletin of the American Meteorological Society, 77(3):437–471. [Kanamitsu et al., 2002] Kanamitsu, M., Ebisuzaki, W., Wollen, J., Yang, S.-K., Hnilo, J. J., Fiorino, M., and Potter, G. L. (2002). Ncep-doe amip-ii reanalysis (r-2). Bulletin of the American Meteorological Society, 83(11):1631–1643. [Kistler, 2001] Kistler, R. e. a. (2001). The ncep-ncar 50-year reanalysis: Monthly means cd-rom and documentation. Bulletin of the American Meteorological Society, 82(2):247–268. [Maheshwari, 1995] Maheshwari, B. L. e. a. (1995). Effacts of regulation on the flow regime of the river murray, australia. Regulated Rivers: research and management, 10:15–38. [Prasad and Khan, 2002] Prasad, A. and Khan, S. (2002). River synopsium in brisbane:murray-darling basin dialogue on water and climate. Synthesis report, Water and Climate Dialogue. [Roads and Betts, 2000] Roads, J. and Betts, A. K. (2000). Ncep-ncar and ecmwf reanalysis surface water and energy budgets for the mississippi river basin. Journal of Hydrometeorology, 1(1):88–94. [Roads et al., 2002] Roads, J., Kanamitsu, M., and Stewart, R. (2002). Cse water and energy budgets in the ncep-doe reanalysis ii. Journal of Hydrometeorology, 3(3):227–248. [Small and Kurc, 2003] Small, E. E. and Kurc, S. A. (2003). Tight coupling between soil moisture and the surface radiation budget in semiarid environments: Implications for land-atmosphere interactions. Water Resources Research, 39(10). 40

[Trenberth, 1998] Trenberth, K. E. (1998). Atmospheric moisture recycling: Role of advection and local evaporation. Journal of Climate, 12:1368–1381.

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Appendice 1: Description in details of the re-analysis used in this study NCEP R1 The NCEP R1 were produced on more than 58 years, from January 1948 to present [Kalnay et al., 1996]. The model used is the NCEP global spectral model. The temporal resolution is 6 hours. The spatial resolution is: • 28 ”sigma” levels in vertical; • T62 model (210 km of horizontal resolution) ; The analysis scheme is a three-dimensional variational (3DVAR) scheme [Kistler, 2001]. The analysed data on a 2.5◦ ∗2.5◦ grid are available from NOAA Web site [http://www.cdc.noaa.gov, ]. NCEP R2 The NCEP R2 were produced on more than 26 years, from 1979 to present [Kanamitsu et al., 2002]. The spatial and temporal resolution is the same than the one used in NCEP R1. The main differences are: • The type of observations used; • An improved assimilation of rainfall, snow and soil wetness; • Human-errors and some of the bugs are fixed. The analysis scheme is the same as in NCEP R1. The analysed data on a 2.5◦ ∗2.5◦ grid are available from NOAA Web site [http://www.cdc.noaa.gov, ]. ERA-40 The ERA-40 re-analysis were produced on 54 years, from September 1957 to August 2002 [Kallberg et al., 2004]. The atmospheric model is known as IFS CY23r4, and is coupled with an ocean wave model. The temporal resolution is 6 hours. The spatial resolution is: • 60 levels in vertical; • T159 spherical-harmonic representation for basic dynamical fields; • A reduced Gaussian grid with approximately uniform 125 km spacing for surface and other grid point fields. The analysis scheme is an updated three-dimensional variational (3DVAR) scheme [Kistler, 2001]. The analysed data on a 2.5◦ ∗2.5◦ grid are available from ECMWF Data Server [http://data.ecmwf.int, ].

42

Appendice 2: Equations Soil moisture index is defined as follow: SM I =

V FMS − PWP FC − PWP

(9)

Where VFMS is the volumetric fraction of moisture in the soil, P W P is the permanent wilting point in fraction by volume and F C the field capacity in fraction by volume. Neither F C nor P W P is a sharply defined quantity. But they can be seen as the upper (F C) and lower (P W P ) limits of soil water that is available to plants. And most of the time, for a soil with a vegetation cover, 0 < SM I < 1.

Lifting condensation level pressure is defined as:  µ

PLCL = P

TLCL T

¶

cp Rd

  =P   

1

56 +

³

ln 1 + Td −56

T

T Td 800

´

 cpd R

     

(10)

Where P is the pressure at the height z, T is the temperature at z, TLCL the temperature at the lifting condensation level, Td is the dew point temperature, cp is the specific heat capacity at constant pressure and Rd is the specific gaz constant for dry air.

Relative humidity: µ

L RH = exp Rv

µ

1 1 − T Td

¶¶

(11)

Where Rv is the specific gaz constant for water vapor and L is the latent heat of phase transition.

43

Figure 23: Mean annual cycle for Madeira Basin of RH and PLCL as a function of SMI in the first soil layer, showing tight coupling [Betts and Viterbo, 2005]. Mean on the period 1990-2001. Data from ERA-40

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Appendice 3: Strength of the coupling for twelve GCMs [Guo et al., 2005]

Model GFDL NSIPP CAM3 CCCma CSIRO UCLA CCSR COLA GEOS BMRC HadAM3 GFS

SW-Precip 0.040 0.034 0.032 0.024 0.014 0.011 0.009 0.009 0.006 0.005 0.002 -0.004

Rank 1 2 3 4 5 6 7 8 9 10 11 12

SW-ET Rank 0.166 1 0.066 4 0.052 8 0.110 2 0.058 5 0.054 7 0.050 9 0.038 11 0.088 3 0.043 10 0.057 6 0.013 12 Table 3:

45

(ET-Precip)1 0.197 0.455 0.685 0.379 0.096 0.294 0.407 0.311 0.143 0.156 -0.038 0.040

Rank 7 2 1 4 10 6 3 5 9 8 12 11

(ET-Precip)2 0.233 0.515 0.593 0.209 0.241 0.200 0.173 0.220 0.068 0.114 0.034 -0.286

Rank 4 2 1 6 3 7 8 5 10 9 11 12

Appendice 4: Worldwide map of the average rainfall (mm.month−1 ) of ERA-40 on the period 1979-2001.

Figure 24:

46

Appendice 5: Climat change for IPSL and GFDL models

Figure 25: Evolution of the three main steps of the soil moisture-precipitation feedback for IPSL: Latent heat flux [W.m−2 ] in function of adimensional soil moisture (A); Rainfall [mm.month−1 ] in function of latent heat flux [W.m−2 ] (B); Adimensional soil moisture in function of Rainfall [mm.month−1 ] (C). Averages on the period 1979-2001, 2029-2049, and 2079-2099.

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Figure 26: Evolution of the three main steps of the soil moisture-precipitation feedback for GFDL: Latent heat flux [W.m−2 ] in function of adimensional soil moisture (A); Rainfall [mm.month−1 ] in function of latent heat flux [W.m−2 ] (B); Adimensional soil moisture in function of Rainfall [mm.month−1 ] (C). Averages on the period 1979-2001, 2029-2049, and 2079-2099.

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Appendice 6: Fictious evolution of the correlation between soil moisture and precipitation in function of the time scale.

Figure 27:

49