Data Consistency Checks - Stochastic Hydrology - Lecture Notes, Study notes of Mathematical Statistics

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(a) Consistency of flow data at a gauge site with the

sum of flows from immediate upstream gauges,

(b) Consistency of flow data with respect to specific

flows,

(c) Consistency of flow data with the flow data at an

immediate neighboring (upstream) station, and

(d) Consistency of the reservoir inflow data where

available, with the data from the surrounding gauge

sites

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Missing data for an example basin:

• The basin is predominantly monsoon driven.
• Flow patterns in the monsoon and non-monsoon

seasons are different.

• Different procedures adopted for filling-up the

discharge data for the two seasons

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Data availability for the basin:

• Daily stream discharge data at 55 gauge sites

available.

• Gauge sites at which short length of data (of less

than 5 years) is available, are discarded from the

analyses.

• 30 gauge sites are selected based on the length of

data availability and location.

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Line Diagram of the Basin

Showing the Location of

Stream Gauge Sites and

Reservoirs

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Monsoon Period (Months: May-September):

Number of years for which data is available is greater

than or equal to 12

Step-1:

• Replace the missing data by average value for that

day, computed from years in which data is available

for the particular day.

Ex: Discharge data for June 20th^ in a year is

missing; Compute the average discharge of June

20 th^ from the data of other years for which the

discharge data is available for June 20th, and fill up

the missing data with this average value

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Monsoon Period (Months: May-September):

Number of years for which data is in between 5 and 12

• If the missing data is non continuous (i.e., not more

than 3 days continuously in a month), plot the daily

flow time series for the month and join the curve

smoothly to obtain the missing values

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If the missing data is continuous (i.e., more than 3

days continuously in a month)

• Compute the proportion of monthly flow occurring

in each day for which the data is missing.

For example, data for six days, June 20-25, 1998

is missing.

Data for all days in June is available for 7 years

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• Use this average proportion on the average of the

month to fill the data for that day

In the example above, let the average of June flow

computed based on 7 years data = 12.6 cumecs

Average proportion for June 20th^ = 0.

Then, the data for June 20th^ 1998 is filled-up as 0.

* 12.6 = 0.252 cumecs

• Similarly fill-up the data for other days in that month.

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Non-monsoon Period (Months: January-April and

October-December):

• Compute the probability that the flow is non-zero for

that day. (Clarke, 1973)

Ex: Day - Oct.20th; Number of years of data available

Number of non-zero flows on Oct. 20th^ in the 6 years

(leaving out the year in which the data is being filled) =

2 (i.e., only 2 out of these 6 years have a non-zero

flow. Remaining 4 years have a zero flow)

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Clarke, R.T. (1973), Mathematical Models in Hydrology, FAO Irrigation and Drainage Paper no. 19, Rome, Italy.

• If the random number is less than the probability of

non-zero flow for that day then it is assumed that a

non-zero flow will occur for that day and the missing

data is replaced with the average value for that day;

Otherwise, the flow for that day is taken as zero

In the example above, the probability of non-zero flows

Random number = 0.

Since 0.248 < 0.333, non-zero flow occurs.

Number of years in which the flow is non-zero = 2

Average flow on Oct. 20th^ based on these two years of

flow = 2.87 cumecs

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Statistical Analysis of Discharge Data:

• Statistical analysis of discharge data is performed

on the data from the selected 30 gauge sites.

• Analyses is conducted over a minimum of 12 years

data starting from 1970

• The Garudeshwar data considered is only for 7

years, from 1970-

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S.No Gauge site (Period)^ used^ Data^ Duratio (years)^ n^ Average (MCum)^ Maximum^ daily flow (cumec)^ Maximum (MCum)^ Minimum (MCum)^ Standard^ deviation (MCum)

Coeff. of variatio n (%) 16 Gadarwara 1977-1999^23 1,304.96 3,080.80 3,016.02 459.23 646.76 50 17 Maheshwar 1985-1993 1996-2000 14 745.17 1,786.00 1,364.76 263.88 299.20 40 18 Bareli 1985-1993 1998-2000 12 756.89 2,964.42 3,749.21 47.10 1,032.01 136 1920 ChhidgaonGinnore 1976-19991971-1999^2429 1,007.022,109.27 (^) 12,157.804,460.00 2,187.604,525.83 249.97553.87 502.53989.50 (^5047) 21 Kogaon 1978-1999^22 1,090.14 4,555.00 2,296.16 164.53 660.65 61 22 Ajandiman 1985-1993 1996-2000 14 255.10 1,149.00 625.33 40.74 183.67 72 23 Tikola 1985-1993 1996-1999 13 532.10 1,398.41 1,738.49 61.34 554.75 104 24 Chandwada 1979-1999^21 1,455.58 7,823.80 4,082.33 149.28 1,097.90 75 25 Sandalpur 1987-1993 1996-2000 12 226.10 779.10 423.89 47.77 133.09 59 2627 BarmanghatBalkheri 1988-19991977-1999 1223 12,642.86722.18 16,283.004,961.10 28,749.001,639.75 4,052.33211.29 6,120.13350.74 (^4849) 28 Barman 1970-1988 1991-1995 24 11,593.41 20,658.20 27,743.94 4,422.63 5,235.99 45 29 Bagratawa 1976-1991^16 1,801.80 9,584.20 5,329.54 61.24 1,383.53 77 30 Gurudeshwar A.M 1970-1976^7 46,756.48 61,000.00 76,885.33 28,104.76 15,774.09 34

Statistics of Annual Flows (contd.)

Statistical Analysis of Discharge Data:

• The coefficient variation is more than 100% for the

gauge sites, Mandla town, Bareli and Tikola,

indicating a high variation of flows

• Similar statistics are computed for monthly flow data
• In non-monsoon months a large variation is

indicated

• As the flow magnitudes are small in the non-

monsoon months, the large variation is not of much

practical significance

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