Data Assimilation for Agricultural Water Management

World’s population is increasing day by day. It will be making water management very critical issue. It has become absolutely necessary to find the solution for effective water management. Many techniques are available for effective water management based on the observed data analysis. Most of the techniques are statistical which are based on collection of data and analysing this data with the help of designing a computational model. For designing the computational model various mathematical and statistical techniques has been used based on state variable equations.

A computational model contains numerous variables that characterise the system being studied. Simulation is done by adjusting these variables and observing how the changes affect the outcomes predicted by the model. The results of model simulations help researchers make predictions about what will happen in the real system that is being studied in response to changing conditions.

Data assimilation is the process by which observations are incorporated into a computer model of a real system. Data assimilation is very important concept of applied mathematics which is used in most of the application areas from signal processing to weather forecasting.

THE BEST ESTIMATE WE CAN MAKE OF ANY PHENOMENON IS PROVIDED BY COMBINING OUR KNOWLEDGE FROM THE PREDICTION AND THE MEASUREMENT.

Predicting something is very hard problem. For solving this problem we need to develop the computational model for future prediction. But only mathematical model cannot give the accurate and significant results. The model should be evolved over time and real world observations should be incorporated into the model to measure the efficiency of the mathematical model. If there are errors in the model means the distraction of the model from the actual observational values, then that errors should be corrected. So we need to incorporate the observations in the model over the period of time.

The figure shows the process of Data Assimilation. 

The purpose of data assimilation is to provide better estimates than can be obtained by only the data or model. Now the question arises why do we assimilate data? The answer is to make a prediction of future pesticides, nutrients and water need to the crop, for this we want to begin with the state of the agricultural field as close to the real field as possible. To understand previous pattern in variability, we want to make the field simulation as close to reality as possible.

Test(1)=A set of soil moisture estimates made by math equations for time=1

Tobs(1)=A set of soil moisture measured in real field at time=1

This is assumed to be “Truth”

Difference=Tobs(1)-Test(1)

Test(2)= Tobs(1)+R*Difference+math,

where R includes

a) Information on errors

b) How to distribute the observed soil moisture to nearby points.

Methods of Model Updating

Input: corrects model input forcing errors or replaces model-based forcing with observations, thereby improving the model’s predictions;

State: corrects the state or storage of the model so that it comes closer to the observations (state estimation, data assimilation in the narrow sense);

Parameter: corrects or replaces model parameters with observational information (parameter estimation, calibration);

Error correction: correct the model predictions or state variables by an observed time integrated error term in order to reduce systematic model bias.

Assimilating moisture data will also cause other variables used for the estimates. The goal is to minimise some measure of difference between the model and the data.

There are two types of DA intermittent data assimilation schemes and continuous assimilation schemes. In intermittent DA data is assimilate after fixed amount of time on a regular schedule, the model is initialised, and a new short-term forecast is made. In continuous assimilation schemes, data is inserted whenever it becomes available. Incremental insertion of data is used over time.

Comparison of prediction with observations is the heart of data assimilation techniques. By comparing we know that the model is close to the truth values.

Modeling the behavior of agro ecosystems is, therefore, of great help since it allows the definition of management strategies that maximize (crop) production while minimising the environmental impacts. Remote sensing can support such modeling by offering information on the spatial and temporal variation of important canopy state variables which would be very difficult to obtain otherwise.