Filtration and assimilation of soil moisture satellite data

*bnn@math.tsu.ru

Filtration and assimilation of soil moisture satellite data

Nikolay N. Bogoslovskiy*, Sergei I. Erin, Irina A. Borodina, Lubov.I. Kizhner Tomsk State University, 36 Lenin Avenue, Tomsk, 634050, Russian Federation

ABSTRACT

This paper presents two data filtration methods. These methods are used for filtration of satellite soil moisture measurement data. A comparison with in-situ soil moisture measurement data shows an improvement in data quality after application of the filters. First results of satellite data assimilation with a global model of numerical weather forecasting are given.

Keywords: data assimilation, surface layer soil moisture, satellite observations

1. INTRODUCTION

In the forecast of the near-surface fields and values in the atmospheric boundary layer it is important to consider properties of the underlying surface. Precision of soil moisture assignment is very important for formation of the sensible and latent heat surface fluxes. In 1996 it was explicitly shown that mistakes in the soil moisture assignment influence significantly the quality of the short-term and medium-term numerical weather forecasting and can even influence seasonal forecasting [1]. However, neither real-time nor regular measurements are being carried out on the meteorological stations. Therefore, it is crucial to estimate soil moisture using other observations and study the possibilities to assimilate these data into numerical weather forecasting models.

Space-based remote-sensing instruments are currently widely used in the whole world; variety of the devices and their overall quantity has increased. Recently several new space-based remote-sensing systems were developed that work in super high frequencies, which allows obtaining surface layer soil moisture allocation, for example, ASCAT [2] and SMOS [3]. Using these satellite remote-sensing data is very attractive and promising as they provide global coverage measurement data and have good horizontal resolution comparable with that of the SL-AV numerical weather prediction model [4,5].

To test the assimilation system and to carry out research ASCAT measurements were used – measurements that are made using the advanced scatterometer installed on the MetOp satellite. ASCAT device allows obtaining measurements with resolution close to 25 km. One of outcomes of these measurements is the surface layer soil moisture which shows level of saturation of the uppermost soil layer (layer no more than 5 cm) and is given in percentage terms from 0 (dry soil) to 100 (moist soil).

2. METHODS OF CONVERSION AND FILTRATION

In order to assimilate satellite data, it is necessary to make a conversion from relative units into volumetric water content, as model uses volumetric units. Conversion method is described elsewhere [6,7]. Studies [7] showed that satellite data has significant oscillation; therefore it is required to additionally filter data.

Two filters were chosen: exponential filter, described elsewhere [8], and Kalman filter[9]. Method consists of two stages:

forecasting and correction. On the forecasting stage one calculates forecast on the system condition (in this case, soil moisture) and covariance errors in real time:

𝑥_𝑘

̂ = 𝐹𝑥̂ + 𝐵𝑢_{𝑘−1 𝑘−1} (1)

𝑃𝑘 = 𝐹𝑃𝑘−1𝐹^𝑇+ 𝑄, (2)

where 𝑥̂ – forecasted soil moisture value in the real time (𝑥_𝑘 ̂ = 0), ₀ 𝑃_𝑘 – errors in the forecasting in the real time (𝑃₀= 1), 𝑄 = 0,00001 – covariation of the process noise, a sufficiently small value, 𝐹 – matrix of the state transition (in case of the dynamic system model), 𝐵 – matrix of the application of an controlling action. Formula (1) allows calculating system condition forecast, (2) – covariation error forecast.

Since we apply this method to the initial data outside the model, 𝐹 is an identity matrix. 𝐵 is a zero matrix, because there is no controlling action over initial data. Therefore, formulas could be simplified:

𝑥̂ = 𝑥_𝑘 ̂ _𝑘−1 (3)

𝑃𝑘 = 𝑃𝑘−1+ 𝑄, (4)

Second stage consists of the forecast correction taking into account model and calculation errors in the real time:

𝐾𝑘= ^{𝑃𝑘𝐻𝑇}

𝐻𝑃_𝑘𝐻^𝑇+𝑅 (5)

𝑥_𝑘

̂ = 𝑥̂ + 𝐾_{𝑘 𝑘}∗ (𝑧_𝑘− 𝐻𝑥̂) _𝑘 (6)

𝑃_𝑘 = (𝐼 − 𝐾_𝑘𝐻) ∗ 𝑃_𝑘, (7)

where 𝐾_𝑘 – Kalman gain, 𝑧_𝑘 – measured value, 𝑅- covariation of the measurement noise (value about 0,005²), 𝐻 – operator shifting from model space to the observations space (consequently, 𝐻^𝑇 – operator shifting from observations space to the model space).

In this case H operator is an identity matrix, because there is no necessity to shift to model space (there is no model in this case). Therefore we have next correction stage for filtering initial satellite data:

𝐾𝑘= ^𝑃𝑘

𝑃_𝑘+𝑅 (8)

𝑥_𝑘

̂ = 𝑥̂ + 𝐾_{𝑘 𝑘}∗ (𝑧_𝑘− 𝑥̂) _𝑘 (9)

𝑃_𝑘= (1 − 𝐾_𝑘) ∗ 𝑃_𝑘, (10)

Given that 𝑥̂ = 0, there are several iterations. 0

3. METHOD OF ASSIMILATION

In order to test the viability of the usage of the satellite measurement data for initialization of the soil variables and evaluate the effect from the utilization of this data in the assimilation system, we used a simplified assimilation scheme based on the optimal interpolation. Assimilation for each grid point is made independently from others.

Let us assume that observation errors and first approximation field errors do not correlate with each other. In this case we can formulate a following equation for finding surface layer soil moisture content analysis field:

( )

a b

K

scat b

      

(11) where



_a – sought surface layer soil moisture content, which will be used as an initial condition in the model;



_scat – surface layer soil moisture content according to satellite measurement data in the point maximally close to the grid point where calculation is being made;



_b – value of the first approximation for the surface layer soil moisture content in the grid point where calculation is being made (as a rule, model forecast on the next 6 hours, made 6 hours ago is used as a background field);

K

– constant that does not depend on space and time.

Using equation 11, we’ll write final expression for the calculation of surface layer soil moisture content analysis field

,1 1 2

,

,2

0.5* * ( ), 1

, 2

b scat b

a l b

F F l

l

  

 

  

    

0.5

0.4

0.3

0.2

0.1

Station Satelite data SWI Filter Kalmans Filter

0.31

I. Dyl

PoAy 5ep2o,1 t'",2oyy

where

l

takes on a value 1 or 2 for surface and deep layer of the soil correspondingly;

F

₁ – function taking on a value of zero if there is a snow cover in the grid point and 1 if snow cover is absent;

F

₂ – function taking on a value of zero if the temperature of the surface soil layer is lower than 273.15 K and 1 if higher than 273.15 K.

4. RESULTS

Figure 1 shows comparison of satellite measurement data with direct measurements made on the Nephi station (39.65˚

N, 111.86˚ E). As is seen from the figure, application of the filters led to decrease in the oscillation of the initial data preserving a quality picture of changes in soil moisture.

Figure 1 – comparison of the satellite data and soil moisture data by Nephi station.

Table 2. Results of satellite data comparison with direct measurements.

Correlation coefficient

ARM (19 stations) COSMOS (34 stations) SCAN (145 stations) Total (198)

Initial data 0.64 0.495 0.454 0.53

SWI 0.721 0.558 0.538 0.60

Kalman 0.722 0.555 0.537 0.60

Absolute error, m³/m³

ARM (19 stations) COSMOS (34 stations) SCAN (145 stations) Total (198)

Initial data 0.018 0.041 0.050 0.036

SWI 0.015 0.0360 0.042 0.031

Kalman 0.015 0.0361 0.0422 0.0311

Root mean square error, m³/m³

ARM (19 stations) COSMOS (34 stations) SCAN (145 stations) Total (198)

Initial data 0.024 0.052 0.064 0.047

SWI 0.02 0.0468 0.0524 0.0397

Kalman 0.019 0.0466 0.0525 0.0393

Relative error, % ARM (19 stations) COSMOS (34 stations) SCAN (145 stations) Total (198)

Initial data 7.3 22.9 37.9 22.7

SWI 6.1 19.87 32 19.3

Kalman 6 19.91 32.1 19.3

0,45

m3/m3

0,4

0,35

0,3

0,25

0,2

0,15

0.1

0,05

o

Comparison of surface soil moisture

-- Assimilation

data

satellite Creek f The station data of Willow Creek

milawith

te data

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PEalitirESIMEWINErdek

!MEIN T6INfIVAMPLI1I

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c <,

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.+ a N ó m N m rv ul m .+ m m o_{m a á} N m NI_{a a in} ul Ñ .+ a n o_{N N N n ñ n n}N m _{W no}N m .+ a n o_{W N N N ó}

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Time ste

Application of both filters had the same positive effect on the initial satellite data. For some stations Kalman filter proved to work better, for others SWI filter. On average the effect of filters application was similar. Table 1 shows averaged results of satellite data comparison with all stations measurements as well as filters effects on the correlation and absolute and relative error. As the result of filters application we managed to decrease errors and increase correlation coefficient.

In order to test effectiveness and precision of the assignment of the initial values of the moisture content in the surface and deep soil layer, the comparison was made with real moisture content measurement data made on AmeriFlux network stations. For this purpose the assimilation of satellite measurement data for July 2012 was being made. The assimilation was made every 6 hours. For the selected stations the comparison was being made between data from stations and moisture content value of the surface and deep soil layers in objective analysis fields. Figure 2 shows comparison of the moisture content for July 2012 for the Willow Creek station (45.80 ˚ N, 90.07 ˚ E). Red line represent data from the station, blue line – data of the moisture content of the surface layer soil without satellite data assimilation. Green line shows moisture content after assimilation of the satellite measurement data. As it visible on the figure, assimilation of the satellite data resulted in decreased error of surface layer soil moisture content initialization. Mean deviation for the Willow Creek station decreased on 0.1 m³/m³, and root mean square error decreased on 0.013 m³/m³.

Similar comparisons were made for 6 more stations (GLEES, OR - Metolius-intermediate aged ponderosa pine, WA - Wind River Crane Site, WI - Park Falls/WLEF, Freeman_Ranch_Woodland, AZ - Santa Rita Mesquite). On average decrease of the mean deviation was 0.07 m³/m³, and decrease of the root mean square error 0.01 m³/m³. Since assimilation of the satellite data is being made only for the surface layer soil, influence on the moisture content of the deep soil layer is insignificant.

Figure 2 – comparison of the surface layer soil moisture.

First results showed that satellite data decrease error in assigning initial values of the surface layer soil moisture,

5. ACKNOWLEDGMENTS

Study is conducted with the financial support of the grant of the President of the Russian Federation MK-6896.2015.5.

REFERENCES

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