Satellite Altimetry of Large Lakes of the Baltic Basin

S. A. Lebedev1,2, Yu.I. Troitskaya3,4, G. V. Rybushkina3 & M.N. Dobrovolsky1

Geophysical Center of the Russian Academy of Sciences1 Molodezhnaya Str. 3, 119296, Moscow, Russia

Space Research Institute of the Russian Academy of Sciences2 Profsoyuznaya Str. 84/32, 117997, Moscow, Russia

Institute of Applied Physics of the Russian Academy of Sciences3 Ul'yanov Str. 46 , 603950, Nizhny Novgorod , Russia

Obukhov Institute of Atmospheric Physics RAS, Moscow, Russia4

Abstract- Variability of the water level of largest lakes in the Baltic Basin is characterized by alternating periods of rise and drop according to the altimeteric measurements of TOPEX/Poseidon and Jason-1/2 satellites. Water level was calculated with the use of an algorithm of regional adaptive retracking for the Lakes Ilmen, Ladoga. Onega and Peipus. Applications of this algorithm considerably increase the amount of actual data records and significantly improve the accuracy of water level evaluation. According to the results, temporal variability of the Lake Ilmen, the Lake Ladoga and the Lake Piepus level is characterized by a wave with a period of 4-5 years and the Lake Onega level we found a wave with a period of 15 years. During the period from 1993 to 2011 lakes level was rising at a rate of 1.17±0.95 cm/yr for the Lakes Il’men’, 0.24±0.10 cm/yr - for the Lake Ladoga, 1.39±0.18 cm/yr - for the Lake Piepus and 0.18±0.09 cm/yr - for the Lake Onega.

I. INTRODUCTION

One of the recent applications of satellite altimetry originally designed for measurements of the sea level is associated with remote investigation of the water level of inland waters: lakes, rivers, reservoirs. A possibility of using altimetry data for determining hydrological characteristics of inland basins is actively studied aimed at determining the hydrological regime of large rivers in South America, Africa and Siberia [1-4], as well as for assessing water level in the lower reaches of the Volga river [5], Volga river reservoirs [6-8] and other inland basins [9]. Numerous applications of satellite altimetry to monitoring of inland waters are reviewed in [10-11]. Standard altimetry data processing developed for open ocean conditions cannot be used in the case of inland waters, where reflection from the land dramatically alters the altimeter waveforms and leads to significant errors in estimation of the water level. Appreciable scatter of satellite data may evidently be explained by the shortcomings of direct extension of the algorithms of water level calculation developed for large water basins (seas and oceans) to medium area basins when the radar return is significantly contaminated by reflection from the land. This effect is very strong in the Volga reservoirs with the width of 10–15 km (except for the Rybinsk reservoir). Under these conditions very few telemetric impulses fit the validity criteria which cause a severe loss of data. The problem of minimization of errors in the water level retrieval for inland waters from altimetry measurements can be resolved by retracking satellite altimetry data. Recently, special retracking algorithms have been actively developed for re-processing altimetry data in the coastal zone when reflection from land strongly affects echo shapes: threshold retracking, β-retracking [12-13], three new retrackers improved the accuracy altimetry observations were proposed in [14]. The latest development in this field is PISTACH (Prototype Innovant de Système de Traitement pour les Applications Côtières et l’Hydrologie) product [15], in which retracking bases on the classification of typical forms of telemetric waveforms in the coastal zones and inland water bodies (see also references in [6-8]. A new method of regional adaptive retracking based on constructing a theoretical model describing the formation of telemetric waveforms by reflection from the piecewise constant model surface corresponding to the geography of the region was proposed in [6-7], where the algorithm for assessing water level in inland water basins and in the coastal zone of the ocean with an error of about 10–15 cm was constructed. This algorithm was tested satellites TOPEX/Poseidon (T/P) and Jason-1/2 (J1/2) at the Gorky Reservoir with complex topography, where the standard Ocean-1 algorithm is not applicable. In [7] a model of an average waveform reflected from a statistically inhomogeneous piecewise constant surface (topographic model) was used for theoretical calculation of the reflected power on the basis of the works [16-17]. The model allowed substantiating criteria of data selection for the Gorky Reservoir. The water level was calculated by means of regional adaptive retracking of the SGDR (Sensory Geophysical Data Record) database for the Gorky Reservoir, and it was shown that application of this algorithm greatly increases the number of included data and accuracy of determining water level. General principles of the proposed algorithm for complicated areas (coastal zones, inland waters, and so on) based on calculations of the signal with allowance for

inhomogeneity of a reflecting surface may be used in different geographical regions. In our work this algorithm is used for reprocessing data for several passes of of T/P and J1/2 satellite in the Lake Ladoga, the Lake Onega, the Lake Il’men’ and the Lake Peipus (Fig.1), the physical geographic parameters of which are presented in Table I. The coastal topography of the lakes is significantly different. Shores of all lakes are primarily low grasslands, forests, wetlands. But the Lake Ladoga and the Lake Onega have a large number of islands. They are located near to northern and north-eastern shores, which are high and sometimes steep. In the presence of additional peaks generated by reflection from land, a smooth coastal water surface and highly reflective coastal objects (buildings, slicks, etc.), the reflected waveforms are poorly approximated by Brown’s formula [16-17], which leads to errors in determining the position of the leading edge and, hence, to wrong determination of satellite altitude and water level. In this case, other quantities, such as wind speed and significant wave height (SWH) are also determined incorrectly. The adaptive algorithm described in [6-7] permits determining the area of satellite pass over the water basin where reflection from the water determines formation of the leading edge of the telemetric pulse and the influence of land is insignificant. The algorithm includes four consecutive steps:

− constructing a local piecewise model of a reflecting surface in the neighbourhood of the lake; − solving a direct problem by calculating the reflected waveforms within the framework of the model; − imposing restrictions and validity criteria for the algorithm based on waveform modelling; − solving the inverse problem by retrieving a tracking point by the improved threshold algorithm.

The adaptive algorithm was tested for reprocessing of the T/P and J1/2 SGDR data in the Gorky and Rybinsk Reservoirs of the Volga River and showed good accuracy of the water level determination [6-7]. Study of the possibility of applying this algorithm for large lakes of Baltic basin is of considerable interest, so as to make it more useful for inland water basins.

Table 1. Physical geographic parameters of the lakes.

Parameter Lake Ladoga Lake Onega Lake Il’men’ Lake Peipus Drainage basin (km2) 276,000.0 66,284.0 67,200.0 47,800.0 Max. length (km) 219.0 245.0 40.0 152.0 Max. width (km) 138.0 91.6 32.0 47.0 Surface area (km2) 17,800.0 9,720.0 982.0 3,555.0 Average depth (m) 51.0 30.0 4.4 7.1 Max. depth (m) 230.0 127.0 10.0 15.3 Water volume (km3) 837.0 285.0 12.0 25.0 Surface elevation (m) 5.0 33.0 18.0 30.0 Shore length (km) 1,570.0 520.0 Islands 660 1,369 29 Islands area (km2) 535.0 30.0 Freezing Period Feb-May Jan.-May Nov.-Apr. Dec.-Apr.

(a) (b) (c) (d)

Fig. 1. Position of T/P and J1/2 satellites groundtracks before (red line) and after (purple line) the maneuver in the water area the Lake Ladoga (a), the Lake Onega (b), the Lake Peipus (c) and the Lake Il’men’ (d). Red points are showed level gauges: Siaskie Ryadki and Balaam (the Lake Ladoga); Petrozavodsk, Voznesenie and Medvezhyegorsk (the Lake Onega); Mustvee and Raskopel (the Lake Peipus); Volkhov-Novgorod, Voytsy and Korostyn (the Lake Il'men’). Yellow line show state boundary between Russian Federation and Estonia.

II. ADAPTIVE RETRACKING OF SATELLITE ALTIMETRY DATA

For modeling the formation of telemetric waveforms in accordance with the procedure of regional adaptive retracking [6], first we construct a piecewise constant model surface (Fig. 2) corresponding to the geography of the region. The model assumed three types of reflected surface: water, land and coastal slicks which are long strips of smoothed water extended along coastlines. Such smoothed regions 20–30 m wide are regularly observed near the coastline (which are usually caused by high concentrations of surface active substances) and are known to give rise to peaks in telemetric pulses [18]. The coastal slicks that were revealed in the Gorky Reservoir water area by field studies can significantly influence the reflected waveforms [7]. In the case of inland water bodies, when the altimeter footprint is a combination of several different (in heights and reflecting properties) parts, the total reflected power is a sum of contributions from all piecewise-constant areas [7]:

( ) ( ) ( ) ( )water land coastP P P Pτ τ τ τ= + + (1)

( )( )

( )( ) ( )( )( ) ( )( )

00

42 22

21 erf

4 2exp 4 2

2kk

k k

i

k k

k

c HPP

h cc H h

s

τ −στ = × + Δϕ

π + + τ− γ + α τ −

⎛ ⎞⎛ ⎞⎜ ⎟⎜ ⎟

⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

(2)

where h is the mean distance from the satellite to the underlying surface. The parameters with index k: Hk, αk, sk correspond to the level, scattering properties and roughness for a given (k-th) part of the underlying surface (Hk, is the deviation of the surface level from the mean value, it is positive when the distance from the surface to the satellite is greater than the mean value and the surface level is lower than the mean value) (Troitskaya et al., 2012b). In (2) we take into account the fact that at time τ = t – 2h/c the main contribution to the reflection from the th illuminated area is given by an arc Δφk centered at the nadir point with coordinates xN, yN and determined by the condition of equality of the distance from the antenna to the k-th piece of surface [7]. The radius of the arc is equal to ( )2 kh c Hτ − and depends on the deviation of the surface level of this

area from the average value. For coastal slicks the reflected power is

( ) ( )( )( )[ ] ( )( ) ( )( )2 2 2(0)2 20

42exp 4 2 exp 2

2N N

wsl sl

sl sl w icsl

x l x y l yc H

h

P dP c H h c dl

h sτ

στ γ α τ τ

π− + −

× − −= − + − −⎡ ⎤⎛ ⎞⎢ ⎥⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦

∫ (3)

where x = x( l ), y = y( l ) is the equation of the coastal line C, dsl is the width of the slick [6]. Using eq. (1)–(3) one can calculate the reflected waveforms and their change when the satellite moves along the track. Parameters in eg. (2), (3) are determined by the properties of the reflecting surface. For the water surface: elevation Hw is water level, s is a significant wave height and σ is determined by the wind speed. For the land surface, H is determined by topography, s is surface roughness, and σ is determined by the reflecting properties of the land. The model was constructed assuming that parameters of land are fixed, and the characteristics of surface water (water level, wave height and roughness) are variable and must be determined using the retracking algorithm.

Based on eq. (1)–(3) the reflected waveforms for each track T/P and J1/2 satellite for all lakes were calculated. For the calculation of waveforms, we choose the model surface parameters from physical considerations: for land σ(0) = 20, α = 10, σs

land = 3 m for water σ(0) = 50, α = 10, σs

water = 0.3 m m for coast slicks σ(0)dsl = 0.5, α = 1000. The parameters specific to the radar altimeter were set equal to γ = 0.0005, τi = 0.425T [6] (T = 3.125·10-9 s – the point target response 3 dB width).

Analysis of the waveforms and their comparison with the waveforms from the SGDR database of Jason-1 enabled us to formulate the first criterion for selecting telemetry impulses for the lakes. We estimated the regions, where the model waveforms are in good

agreement with the measured ones, and the leading edge of the waveforms is determined by the reflection from the water surface. In addition to the first criterion, in accordance with the long-term observations at level gauges, the deviation of the water level from an average value by more than 2-4 m should be considered erroneous. For the valid waveforms we used regional retracking algorithms appropriate for the lakes, including 2 steps. At the first step we

kϕΔ

Fig. 2 Piecewise constant model of underlying surface (+ denotes the position of nadir, the red dotted line denotes the track of the satellite, the red circle denotes the border of illuminated area at a given time, the pale blue area denotes water, the blue area denotes slick or rush and the yellow and green areas denote different types of land - swamp or forest)

estimate a tracking point determined by a definite threshold. The second step is refinement of the estimates: the alleged weak leading edge – 4 points in the neighbourhood of the threshold (see Fig. 12 in [7]) are fitted by the error function (taking into account the analytical results):

1+erf RAS

⎛ τ − τ ⎞⎛ ⎞⎜ ⎟⎜ ⎟

⎝ ⎠⎝ ⎠ (4)

The parameters in (4) are retrieved by minimization of root-mean-square deviations. The minimization procedure was slightly modified in comparison with [7]. To improve the algorithm convergence the initial value of the parameter s, which characterizes SWH on the water surface, was estimated from the mean slope of the leading edge of the waveform. The signal amplitude A is found by averaging the values of the power over several points, following the leading edge. Then the parameter τR characterizing the arrival time of the reflected signal is determined by the one-parameter optimization. The modified optimization algorithm provides a more accurate value for the tracking point τR.

III. RESULTS AND DISCUSSION

The water areas of the large lakes of the Baltic basin are intersected by several ground tracks of T/P and J1/2 altimetry satellites (Fig. 1). The water area of all lakes is sufficiently large and the reflection conditions are similar to the oceanic area with the exception of the coastal areas and the areas near islands (especially true for the Lake Ladoga and the Lake Onega (Tab. 1)). But the ground tracks often pass near the shore lines and islands, which may lead to the pronounced influence of land reflection on the waveforms of the received telemetric pulses and appropriate errors in water level. Therefore it is interesting to calculate the water level on the algorithm of regional retracking to compare results with in-situ level gauge data. The results of the computations showed that satellite altimetry data correspond to gauge level with a determination coefficient equaled to 0.97-0.98. This result allowed us to make some important conclusions about the water level variability. According to computations (Fig. 3), temporal variability of the Lake Ilmen level is characterized by a wave with a period of 4-5 years (maximum in 2001, 2004, 2008 and minimum in 1997, 2003, 2008). Between 2000 and 2011, the lake level raised at a rate of 1.17±0.95 cm/yr. The level of the Lake Ladoga also showed a wave with period 4-5 years (maximum in 1995, 1999, 2005, 2010 and minimum in 2003, 2006, 2009). From 1993 to 2011 the lake level was decreasing at rate of 0.24±0.10 cm/yr. Similar wave is observed in the Lake Piepus level (maximum in 1995, 1999, 2005, 2010 and minimum in 1997, 2003, 2008). During the period from 1993 to 2011 its level was rising at a rate of 1.39±0.18 cm/yr. In the interannual variability of the Lake Onega level we found a wave with a period of 15 years (maximum in – 1995, 2009 and minimum in 2003). From 1993 to 2011 the lake level was decreasing at a rate of 0.18±0.09 cm/yr.

1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012Date (year)

-150

-100

-50

050

100

150

Lake

Lev

el A

nom

aly

(cm

)

Lake Ladoga

1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012Date (year)

-150

-100

-50

050

100

Lake

Lev

el A

nom

aly

(cm

)

Lake Onega

(a) (b)

(c) (d)

2000 2002 2004 2006 2008 2010 2012Date (year)

-300

-200

-100

010

020

030

040

0

Lake

Lev

el A

nom

aly

(cm

)

Lake Il'men'

1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012Date (year)

-150

-100

-50

050

100

150

Lake

Lev

el A

nom

aly

(cm

)

Lake Peipus

Fig. 3 Temporal variability water of the Lake Ladoga (a), the Lake Onega (b), the Lake Peipus (c) and the Lake Il’men’ (d) based on altimetric measurements T/P and J1/2 satellites.

The local adaptive retracking algorithm enables retrieving water level even in the case of sufficiently small water basins with a very complex reflecting surface. It works well for both T/P and J1/2 SGDR data. Application of the algorithm increases significantly the number of valid data and improves dramatically accuracy of the water level retrieval from the altimetry data. The problems of inland water data processing are very similar to those arising in the coastal zones of the ocean and other complex areas from contamination of the received signal by reflection from the land. Therefore the adaptive retracking algorithm based on calculations of the waveforms taking into account inhomogeneity of the reflecting surface adjusted to a certain geographic region allows constructing a step-by-step strategy for improving estimations of water level and other hydrological parameters in such areas.

ACKNOWLEDGMENT

This study was supported by a series of grants of the Russian Foundation for Basic Research (No 13-05-01125 and 14-05-00644).

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