Importance of representing the physics of the soil surface correctly
Land surface model helps us to understand the processes that trigger the precise climate in a region, by analyzing its internal interactions. We are able to understand the current climate locally but also the factors that generate a specific climate in other regions. Fluxes between soil and the atmosphere can have non-local effects. In addition, climatic conditions into the future can be predicted. Its accuracy depends on the degree of precision with which the model represents the physics reality and the assumptions about the future factors that climate will encounter. Furthermore, LSM provides data not directly available or difficult to interpolate. Models compute different estimates answering questions about what processes will affect a particular region in the future.
Challenges in LSM representation
The land surface physics includes an extensive collection of complex processes. The balance between model complexity and resolution, subject to computational limitations, represents a fundamental question in the development of LSM. By increasing the comprehension of physical phenomena, LSM can grow into a more complex model adding new processes extrapolated from the environment. In the next section, some of the complexities found in most LSM are presented.
The soil is a complex environment. Its composition includes inorganic and organic particles that determine its inherent characteristics. Its ability to retain water and its density varies drastically depending on the percentage of primitive components (sand, silt, or clay) or structure (ash, fine, or coarse sand). There may be several types of soil in a small area, with their associated features, especially water content. Omission of surface spatial heterogeneity in a LSM can cause errors in flux estimation (Courault et al., 2010, Olioso et al., 2005). Spatial variations in surface heterogeneity are imperative in order to guarantee an accurate simulation of the land-surface fluxes. The sub-grid scale land surface heterogeneity must be parameterized in the surface scheme so that the land characteristics are accounted for in the model (Manrique et al, 2013).
State of the art in the use of LST to constrain LSM
Several works regarding the calibration of LSM based on LST measurements demonstrate the improvement in fluxes estimation, when constraining model parameters.
In Castelli et al. (1999), a variational data assimilation approach is used to include surface energy balance in the estimation procedure as a physical constraint (the adjoint technique). The authors work with satellite data, where soil skin temperature is directly assimilated. As a conclusion, constraining the model with such observation improves model fluxes estimations, with respect to in situ measurements.
In Huang et al. (2003) the authors developed a one-dimensional land data assimilation scheme based on ensemble Kalman filter, used to improve the estimation of soil temperature profile. They conclude that the assimilation of LST into land surface models is a practical and effective way to improve the estimation of land surface state variables and fluxes.
Reichle et al. (2010) performed an assimilation of satellite-derived skin temperature observations using an ensemble-based, offline land data assimilation system. Results suggest that retrieved fluxes provide modest but statistically significant improvements. However, they noted strong biases between LST estimates from in situ observations, land modeling, and satellite retrievals that vary with season and time of day. They highlighted the importance to take these biases properly, or else large errors in surface flux estimates can result. In Ghent et al. (2011), the authors investigate the impacts of data assimilation on terrestrial feedbacks of the climate system. Assimilation of LST helped to constrain simulations of soil moisture and surface heat fluxes. Another study by Ghent et al. 2011, investigates the effect that data assimilation has on terrestrial feedbacks to the climate system. The authors state that representation of highly complex biophysical processes in LSMs over highly heterogeneous land surfaces with limited collections of mathematical equations, and the tendency of over parameterization, infers a degree of uncertainty in their predictions. Assimilation of land surface temperature (LST) to constrain simulations of soil moisture and surface heat fluxes can be integrated into the model to update a quantity simulated by the model with the purpose of reducing the error in the model formulation. The correction applied is derived from the respective weights of the uncertainties of both the model predictions and the observations. The results found in this research suggest that there is potential for LST to act as surrogate for assimilating other state variables into a land surface scheme.
Ridler et al. (2012) tested the effectiveness of using satellite estimates of radiometric surface temperatures and surface soil moisture to calibrate a Soil–Vegetation–Atmosphere Transfer (SVAT) model, based on error minimization of temperature and soil moisture model outputs. Flux simulations were improved when the model is calibrated against in situ surface temperature and surface soil moisture versus satellite estimates of the same fluxes.
In Bateni et al. (2013), the full heat diffusion equation is employed as constrain, in the variational data assimilation scheme. Deviations terms of the evaporation fraction and a scale coefficient are added as penalization terms in the cost function. Weak constraint is applied to data assimilation with model uncertainty, accounting in this way for model error. The cost function in this experience contains a term that penalizes deviation from prior values. When assimilating LST into the model, the authors proved that the heat diffusion coefficients are strongly sensitive to specific deep soil temperature. As a conclusion, it can be seen that the assimilation of LST can get a remarkable improvement in the model simulated flows.
The SECHIBA version used in this work models the hydrological budget based on a two-layer soil profile (Choisnel model, 1977). The soil layers correspond to the surface and the bottom of the soil. The total depth of the layers corresponds to the plants root depth. The soil has a unique type, with a total depth of dpucste = 2m. The bottom layer of soil acts like a bucket that fills with water from the top layer. When the top layer is empty with no water (due to evaporation, drainage to the lower layer, or lack of precipitation), this layer disappears. When rainfall exceeds the evaporation losses, they recreate a wet surface, allowing it to evaporate. If the water quantity is about to saturate the two soil layers, the top layer disappears again and excess water is removed by runoff. The soil fluxes, as they are modeled in SECHIBA, are presented in Fig 2.2. The different operations to obtain the fluxes are summarized in Table 2.3.
Representing a model and its adjoint through a modular graph
The description of this section is based on the work by Nardi et al, 2009. Considering the case of a discrete physical model (atmospheric, oceanic or other), the state evolution in space between two consecutive time steps is governed by a discrete model of evolution: the direct model M. As an example, we consider here the case of a model in two spatial dimensions. A state variable is denoted by xij(t) where i, j are the spatial coordinates on a mesh and t the time index. The discretization leads to a numerical expression for each variable xij(t), which gives its functional dependence on other variables that may be located on any points of coordinates. These dependencies result in a sequence of functions corresponding to a simple modular graph.
A modular graph is a set of interconnected modules. The modules represent the nodes of the graph. A directed arc from Fp module to Fq means that Fp transmits a portion of its output to Fq. We also define:
Module: A module F is a computational entity; it receives an input vector and computes an output vector. A graph is formed by several modules; a module receives its inputs from other modules or from the external environment, and transmits data at the output of the other modules or to the outside environment.
Basic connection: we schematize the transmissions between modules with connections called basic connections. They link the ith output of module Fp to the jth input of Fq module, indicating that the ith value calculated by Fp is transmitted to the jth of Fq. Transmission of data outside or inside the graph will be represented by a basic connection starting from the outputs of some of the modules. A physical model M is represented by a modular graph, denoted by Γ.
In Fig.3.2 a subset of modules is represented as an interconnected graph. Fp module transmits the output yp1 to the input xq1 of module Fq and output yp2 to input xq2. The same output yp2 will also be sent to input xl1 of module Fl; equally for the other modules. Fig.3.2.a represents the basic connections describing the transmission of data between modules. Fig.3.2.b represents the modular graph. In general, an arc of a modular graph represents several basic connections.
Table of contents :
CHAPTER 1 INTRODUCTION LAND SURFACE MODELS. OBJECTIVES AND ORGANIZATION OF THE THESIS
1.2 COMPONENTS OF LAND SURFACE MODELS
1.2.1 WATER PROCESSES
1.2.2 SOIL THERMODYNAMICS
1.3 IMPORTANCE OF REPRESENTING THE PHYSICS OF THE SOIL SURFACE CORRECTLY
1.4 CHALLENGES IN LSM REPRESENTATION
1.4.1. SURFACE HETEROGENEITY
1.4.2 NUMERICAL REPRESENTATION
1.4.3. MATHEMATICAL REPRESENTATION AND MODEL CALIBRATION
1.5 THESIS CHALLENGES
1.5.1. STATE OF THE ART IN THE USE OF LST TO CONSTRAIN LSM
1.5.2 GENERAL OBJECTIVES
CHAPTER 2 DESCRIPTION OF THE LAND SURFACE MODEL ORCHIDEE AND DATASETS
2.1.2 BIOSPHERE CHARACTERIZATION
2.2.2 ENERGY BUDGET
2.2.3 HYDROLOGICAL BUDGET
2.2.4. SECHIBA PARAMETERS
2.3.1. EDDY COVARIANCE MEASUREMENTS
CHAPTER 3 THEORETICAL PRINCIPLES OF VARIATIONAL DATA ASSIMILATION
3.1 INTRODUCTION AND NOTATION
3.2 ADJOINT METHOD
3.3. REPRESENTING A MODEL AND ITS ADJOINT THROUGH A MODULAR GRAPH
3.3.1. DEPLOYMENT OF A MODULAR GRAPH
3.4. DIAGNOSTIC TOOLS FOR THE ASSIMILATION SYSTEM
3.4.1 TEST THE CORRECTNESS OF THE ADJOINT MODEL
3.4.2. TEST THE CORRECTNESS OF THE COST FUNCTION GRADIENTS
3.4.3. DERIVATIVE TEST
CHAPTER 4 THE YAO APPROACH: THEORETICAL ASPECTS AND IMPLEMENTATION OF SECHIBA-YAO 1D
4.2 YAO APPROACH
4.3. CREATING A PROJECT WITH YAO
4.3.1 INPUT / OUTPUT MANAGEMENT
4.3.2 DIAGNOSTIC TOOLS FOR THE GENERATED PROJECT
4.4. DEVELOPMENT OF SECHIBA-YAO 1D
4.4.1 IMPLEMENTATION OUTLINE
4.4.2 DIRECT MODEL VALIDATION
4.4.3 ADJOINT MODEL VALIDATION
CHAPTER 5 SENSITIVITY ANALYSIS OF THE SECHIBA-YAO 1D MODEL USING FLUXNET DATASET
5.2 VARIATIONAL SENSITIVITY ANALYSIS
5.2.1. SENSITIVITY ANALYSIS WITH LAND SURFACE TEMPERATURE
CHAPTER 6 TWIN EXPERIMENTS WITH SECHIBA-YAO 1D USING FLUXNET MEASUREMENTS
6.2 EXPERIMENT DEFINITION
6.3.1 EFFECT OF THE OBSERVATION SAMPLING
6.3.2 EFFECT OF RANDOM NOISE IN THE OBSERVATION
6.3.3 EFFECT OF THE CONTROL PARAMETER SET SIZE
CHAPTER 7 REAL MEASUREMENTS STUDY USING SMOSREX DATASET
7.2 KEY PARAMETERS TO PERFORM THE OPTIMIZATION
7.3 LST DATA ASSIMILATION WITH PARAMETER STANDARD VALUES
7.3.1. SIMULATED VS. OBSERVED MEASUREMENTS
7.3.2. BRIGHTNESS TEMPERATURE SENSITIVITY ANALYSIS
7.3.3. BRIGHTNESS TEMPERATURE ASSIMILATION DURING A SINGLE DAY
7.3.4. BRIGHTNESS TEMPERATURE ASSIMILATION DURING A WEEK
7.4 LST VARIATIONAL DATA ASSIMILATION WITH DIFFERENT PRIOR VALUES
7.4.1. SIMULATED VS. OBSERVED MEASUREMENTS
7.4.2. BRIGHTNESS TEMPERATURE SENSITIVITY ANALYSIS
7.4.3. BRIGHTNESS TEMPERATURE ASSIMILATION DURING A SINGLE DAY
7.4.4. BRIGHTNESS TEMPERATURE ASSIMILATION DURING A WEEK
7.5. ANALYSIS OF THE ASSIMILATION SYSTEM THROUGH TWIN EXPERIMENTS
CHAPTER 8 CONCLUSION AND PERSPECTIVES